You may need to work at giving her a different answer (still vague), but if you continue to say "just friends" she is going to think you are faking the whole thing. You could say something like, "Why the sudden interest in my life, when you no longer want to be a part of it"? (But don't let that lead to a R talk, turn and walk away). Or you could dryly say, "I don't ask you questions about your personal time". She is choosing to give up her rights as your W, and that includes asking for details. She needs to know it. So, don't continue saying the same thing, b/c it does sound pretty phony......even if it's not. However, don't start giving her names!
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!