Nice story. It's an interesting idea and you put in the work to develop it. It works overall as an idea, but I think there are a few flaws. Some comments:
Does it matter that Judy is short for Judith? Do we need to be told that twice?
The fun of this premise, to me, is in exploring the daring places people will go when they are roleplaying. The reader gets to enjoy both the surface-level eroticism, the tension of the role-play, and also the characters experiencing the breakdown of their own inhibitions.
However, when Judy says "You're looking for a place to park with me, aren't you?", the role-play breaks down a bit. Let me explain. If Judy is in character here, it's obviously too forward a gambit and breaks plausibility; if this is the real Judy breaking character to figure out what's going on, this disrupts the flow of the fantasy for the reader. More effective would have been Judy's character expressing nervousness or subtle delight at this potentially predatory, rushed encounter.
Later, again, Judy says "I get that. You know what I often say; look like a good girl but act like a bad one." The "often" indicates we are out of role-play now, but we slip back into role-play in the next paragraph when describing "first dates". At this point I'm not invested in the characters your characters are playing any longer.
This line is confusing: "When I came she swallowed it all, which she would do periodically." Does this mean she swallowed periodically during this ejaculation, or that this is an occasional habit of hers in other sexual encounters? If it's the latter, we have again broken character.
I think that the story would be much better if the two keep in character for the entirety of the role-play. It can be effective if there is some breakdown of the role-play during the sex itself, as this introduces the erotic potential of misunderstanding and cross-purposes, but to have so many interruptions throughout the role-play was not effective, in my opinion.
The sex itself is described in very broad strokes. That's fine if the sex itself is incidental to the erotic interplay of the two characters, but if you want to arouse the reader, I think you need to hook us with some more concrete details about the physicality of it all.
The literary references might make sense to you, but they really don't enlighten the reader or add to the scene.
A few grammar issues, if you want feedback on that:
"I might be interesting in joining the paper myself." > should be "interested"
"His kisses were softer and friendlier than Michelle's" > his? hers?
She said, "Now were back to normal. > missing close quote; should be "we're"