When it comes to whether or not to accept the request, you really have to consider the girlfriend herself, not your past experience. Does the boyfriend already seem to have several (unrelated) female friends? Is the girlfriend a little/some/not at all possessive? If any of these factors made me feel uncertain, I think I would go the route of ignoring the request and see if the subject is ever broached by either of them. It's better to be safe and respect the friendship.
When it comes to the past relationship, which I understand has already been brought up and addressed, I have a strong opinion. And, I see that a lot of folks are saying - if she can't handle you talking to her man, too bad for her. I am a woman whose husband has a very close relationship with two of his ex-girlfriends, with one of whom he was VERY much in love at the time, and I'm fine with the relationships. But, I say that a woman going to another "woman's man" as it were, about HER relationship with another man is an implied invitation.
You can disagree with me all you want, and I am very open to friendships of either sex for either partner in a relationship, but it is my unwavering opinion that girls should talk to their girls about guy problems. And you can even talk to your single male friends about your guy problems (although I feel like you are playing with fire, even there - "oh sweetie, I would NEVER treat you like that, do that to you, etc....") But, your relationship problems should not be laid bare with another woman's man, ESPECIALLY in the other woman's absence.
Best of luck to you in making a wise decision,
B.