Well I'm not quite sure what to think of this situation. My ex and I dated for two and a half years broke up then were off and on until Christmas when we broke up. She started dating someone else two weeks after we broke up. We have talked a couple times since then, just not regularly. Three days ago, however, she made it her personal goal to have a non-stop conversation with me. For example if I forget to text back she'll text me thirty minutes later to start another conversation about something completely irrelevant. I did turn it into a game to see how many times she would attempt to start a conversation about nothing. Moreover, I feel badly about the whole situation because I am sure her boyfriend would be unhappy with what she was doing if he knew. It is obvious that she is seeking an unreal amount of attention(she is super maintenance) but I still am unsure about her intentions.
Did she actually say, "It's my personal goal to have a non-stop conversation with you"? All kidding aside, it sounds like she's just seeking attention. Maybe she still has feelings for you. Do you still have feelings for her? Ultimately, do what's best for you. If you feel that her texting you is driving you insane, tell her to stop. Also, bring it up to her that maybe this type of activity would bother her boyfriend.
I see what you did there. Sounds to me like she might want you back. Ask if her boyfriend knows she's talking to you, and whether or not she thinks he'd be bothered/is bothered by it. You'll probably be able to judge her intentions by this, because if she says he doesn't know and would be bothered by it if he did, than to me she's not risking her new relationship for random small talk with an ex, it's more like she just wants to talk to you regardless of whether it gets her in deep shit with the other guy. If you want a quick answer, just tell her you don't feel comfortable talking to her so often since you're the ex and she has a new boyfriend. She'll tell you the real reason she's talking to you so much if she cares, and if she doesn't care/just wants attention, she'll probably back off.