Well done on getting the meeting with her! Was it Stella Creasey who didn't believe that AGP exists and said that it was transphobic to mention it? (AKA 'I don't want to look at any evidence that might challenge the view that I think I should have').
I would start by stressing that you appreciate that the proposals for self-ID were well intentioned, but that this will bring unintended consequences which are simply being ignored. What's more, there is a concerted effort to prevent these concerns being discussed, which is extremely worrying (you could mention the Millwall/HoC venue change and the harassment the HoC received, as she will surely be aware of this and can easily verify it if not).
Have some clear examples of the consequences. Sport is a good one, as this is easily verifiable (eg Fallon Fox, Laurel Hubbard, Andrea Yearwood), would strike most people as being unfair/downright cheating, and is also a response to any claims that 'there are no problems in other countries'.
Say that you'd like her to think about what exactly she is asking other women to do. Ask her why changing rooms are segregated by biological sex. Does she agree that women are particularly vulnerable when they are naked? Does she agree that most women would not want to be naked/in a state of undress in front of men who they are not in a relationship with? Ask her why, then, is she telling women to do just that? Why, in the light of the #MeToo campaign, is she telling the country that women's boundaries shouldn't be respected?
If she says that transwomen are not safe in men's changing rooms, ask her why. Does she agree that it is because some men are violent and attack random strangers? Does she agree that it is not all men, but we don't know which ones as they don't wear a badge? Does she agree that women, who are smaller and weaker than men, have even less chance of defending themselves against a male-bodied attacker? Why then, is she telling women that their safety doesn't matter?
Continuing with the changing rooms angle, go back to the 'some men are violent' bit. Reiterate that the problem is male violence, so what does she plan to do to make the men's facilities safe for all men? Where are the campaigns urging men to welcome gender non-conforming men into their facilities? Why aren't men being targetted to sort this out? Stress that you absolutely applaud stereotypes being broken, and that people should of course be free to dress how they want to without discrimination - but that this will not happen until men accept gender non-conforming men. This is a male problem and it needs a male solution. Entry to women's facilities should never be treated as the answer.
Good luck!