This is always a tough one, but one thing to keep in mind is that while well meaning, many people think kids are made out of 200 year old glass that will break if you blow on it...and they aren't. To be honest, I think your kids will have a hard time if you are in a new relationship, male or female, because they have gone through a divorce, and in many ways I suspect that may be a bigger issue then the fact you are seeing another woman. They may use the fact that she is a woman as an excuse to try and wreck your relationship, but a lot of it could well be being with anyone. I obviously don't know where you are with the divorce, did it happen recently, did it happen a while ago, and that could matter.
And yes, it can be difficult on kids when their parent is different, I have seen this one and experienced it, both with gay parents, parents where one or the other ends up with a same sex partner, and transgender people with children, and in the end, the funny part is the kids usually end up okay, as tough as it can get. People can be cruel, it is ironic that the only place where the kids who have parents who are same sex or have a parent who ends up in a same sex marriage is the cruelty from other assholes who make their lives difficult, it is ironic that many of the 'traditional family values' try to create a self fulfilling prophecy, in that they see no problem in making the lives of kids of LGBT parents tough, then try to claim being the children of gay parents hurts them, when it is assholes like themselves who hurt them.
Okay, so back to the OP's original question, I tend to agree with others, I think one of the keys is being sure of yourself, that if/when you 'come out' as being with another woman, you are comfortable with it. I am not talking when you are together with your sweetie, but being comfortable deep down that you are okay with it, you don't find it weird, and can deal with it if other people, whether it is your ex or others, get nasty. Kids care about what others think, but they care more about their parent, and they tend to pick up, not what we say, but what we project. The parent who tells their kid they are colorblind but then when they meet someone who is black tense up, or act differently, the kids will pick it up. I really encourage you to work with an LGBT friendly counselor, to work on being comfortable yourself and in how to come out to the kids. Actually, I would probably tell you to find a counselor even if it was a guy, to deal with the kids and their feelings, it isn't all that much different.
In terms of telling the kids, one of the biggest mistakes people make IMO is over doing it, insisting on telling every detail. If you have a girlfriend you are serious about (and I note she said she loved you, but how do you feel about her, OP? If you aren't certain of your feelings for her, that it is strongly reciprocated, I wouldn't tell at this point). I don't like the idea of saying she is a friend, kids aren't stupid and they pick up the clues, they will know long before you tell them if you do that IMO, and will probably be more resentful you wouldn't tell them. But don't belabor it, either, it is okay to say you and X are dating, that you have strong feelings with her, and leave it at that. You don't need to bring up labels, to be honest, they don't matter, you don't have to tell them "I am lesbian' or 'I am bi', it isn't valuable to do so, simply tell them you have someone you are seeing and they are special to you, period.They may have questions, they may ask how long you have known her, they may ask if you plan to live together (which, to be honest, I would tell them not for the forseeable future, you have enough to deal with). You can also reassure them that while there is nothing shameful about your relationship, that you also don't plan on making a big deal about it, that eventually people will know,but you plan on being low key. Obviously, a lot of this depends where you live, if you were in San Francisco or Park Slope, Brooklyn or Portland Oregon it would be a no brainer, if you live in South Boston, Alabama (if there is such a place), might be different. I also would check with a lawyer, to make sure you don't live in one of the garden spots, like Alabama and some other places in the hookworm belt, where your husband could try and get custody of the minor child and with a good chance of winning simply because you are with a woman, that would be wise IMO.
But like I said, in the end things usually work out well. If you and your kids have a good relationship, if you have good communication and such, it will be fine. A friend of mine transitioned (M to F) with two teenage boys, in a fairly conservative suburb of NYC, and she did fine with them, her boys faced it pretty well, and surprisingly, the other kids rallied around the sons, and their house was a pretty popular place to hang out...so it happens. I had my own coming out process before I stopped transition, and I can tell you there will be people who will give you and your kids a hard time, but a lot of people are going to surprise you. If your husband gets wind and is negative about it, don't let him give you shit about it, he has no right to decide what you do. This is where a therapist comes in, they will be able to help you with that, how to deal with the husband, etc. In terms of the legal issues, there are LGBT legal resources all over the country who can help if push comes to shove, so even that doesn't have to be scary.
What it all boils down to,to summarize is if this relationship is serious and you are comfortable it is, the rest probably will fall into place, and I can assure you that coming from this place of strength, your kids will be fine, they are resilient and if they see you are happy and comfortable, they will adjust. It can be rocky, always is with teenagers, but I know a lot of people in your position, gay and trans, and most of them end up okay with their kids in the end.
And yes, it can be difficult on kids when their parent is different, I have seen this one and experienced it, both with gay parents, parents where one or the other ends up with a same sex partner, and transgender people with children, and in the end, the funny part is the kids usually end up okay, as tough as it can get. People can be cruel, it is ironic that the only place where the kids who have parents who are same sex or have a parent who ends up in a same sex marriage is the cruelty from other assholes who make their lives difficult, it is ironic that many of the 'traditional family values' try to create a self fulfilling prophecy, in that they see no problem in making the lives of kids of LGBT parents tough, then try to claim being the children of gay parents hurts them, when it is assholes like themselves who hurt them.
Okay, so back to the OP's original question, I tend to agree with others, I think one of the keys is being sure of yourself, that if/when you 'come out' as being with another woman, you are comfortable with it. I am not talking when you are together with your sweetie, but being comfortable deep down that you are okay with it, you don't find it weird, and can deal with it if other people, whether it is your ex or others, get nasty. Kids care about what others think, but they care more about their parent, and they tend to pick up, not what we say, but what we project. The parent who tells their kid they are colorblind but then when they meet someone who is black tense up, or act differently, the kids will pick it up. I really encourage you to work with an LGBT friendly counselor, to work on being comfortable yourself and in how to come out to the kids. Actually, I would probably tell you to find a counselor even if it was a guy, to deal with the kids and their feelings, it isn't all that much different.
In terms of telling the kids, one of the biggest mistakes people make IMO is over doing it, insisting on telling every detail. If you have a girlfriend you are serious about (and I note she said she loved you, but how do you feel about her, OP? If you aren't certain of your feelings for her, that it is strongly reciprocated, I wouldn't tell at this point). I don't like the idea of saying she is a friend, kids aren't stupid and they pick up the clues, they will know long before you tell them if you do that IMO, and will probably be more resentful you wouldn't tell them. But don't belabor it, either, it is okay to say you and X are dating, that you have strong feelings with her, and leave it at that. You don't need to bring up labels, to be honest, they don't matter, you don't have to tell them "I am lesbian' or 'I am bi', it isn't valuable to do so, simply tell them you have someone you are seeing and they are special to you, period.They may have questions, they may ask how long you have known her, they may ask if you plan to live together (which, to be honest, I would tell them not for the forseeable future, you have enough to deal with). You can also reassure them that while there is nothing shameful about your relationship, that you also don't plan on making a big deal about it, that eventually people will know,but you plan on being low key. Obviously, a lot of this depends where you live, if you were in San Francisco or Park Slope, Brooklyn or Portland Oregon it would be a no brainer, if you live in South Boston, Alabama (if there is such a place), might be different. I also would check with a lawyer, to make sure you don't live in one of the garden spots, like Alabama and some other places in the hookworm belt, where your husband could try and get custody of the minor child and with a good chance of winning simply because you are with a woman, that would be wise IMO.
But like I said, in the end things usually work out well. If you and your kids have a good relationship, if you have good communication and such, it will be fine. A friend of mine transitioned (M to F) with two teenage boys, in a fairly conservative suburb of NYC, and she did fine with them, her boys faced it pretty well, and surprisingly, the other kids rallied around the sons, and their house was a pretty popular place to hang out...so it happens. I had my own coming out process before I stopped transition, and I can tell you there will be people who will give you and your kids a hard time, but a lot of people are going to surprise you. If your husband gets wind and is negative about it, don't let him give you shit about it, he has no right to decide what you do. This is where a therapist comes in, they will be able to help you with that, how to deal with the husband, etc. In terms of the legal issues, there are LGBT legal resources all over the country who can help if push comes to shove, so even that doesn't have to be scary.
What it all boils down to,to summarize is if this relationship is serious and you are comfortable it is, the rest probably will fall into place, and I can assure you that coming from this place of strength, your kids will be fine, they are resilient and if they see you are happy and comfortable, they will adjust. It can be rocky, always is with teenagers, but I know a lot of people in your position, gay and trans, and most of them end up okay with their kids in the end.