NP here and an MB.
While I agree that you should NOT suck it up, I do think you made a mistake early in the process by not bringing it up earlier. Once you said "we have to discuss this further", it became your responsibility to bring it up in the interview. Obviously, she wants to pay the rate she wants to pay, so it isn't in her interest to bring it up in the interview. You wanted a different rate, and as such, you need to advocate for yourself as soon as possible in the process so you work this out, or both move onto other opportunities.
If you tried to negotiate with me at this, after not bringing it up in the interview, I'd be annoyed and wonder why you bothered to continue to interview when you knew our terms didn't match. On the other hand, if you had brought it up in the interview, I'd probably be more open to salary negotiations.
I'm not saying that she *should* refuse to negotiate with you now. I'm just saying that you need to advocate for yourself early, as she already is by asserting the rate she wants to pay, and not expect her to bring up a topic that will cost her money.
That said, good luck and I hope it all works out for you.