I'm a lawyer so I look at this from a contract perspective. Warning-- I didn't do so well in contracts in law school and I don't practice law in this area, so who knows if I have this right or not. Not giving legal advice or acting as your lawyer, you know

You have a mutual understanding that you have a 45 min or so session and you pay whatever you pay per session, $125? If she's going to change the terms of the contract, then she has to alert you to that and explain the new "offer", which you can either accept or not accept. What she should have done is after 50 minutes, said something like. "Our time is up for a 45 minute session. I can let you have another 15 minutes, but I will have to bill you an extra $75. What would you like to do?"

Me: I'd like to go now and save $75. See you next week.

Or you could say, "that's fine. I'd like to finish my thoughts and I'm okay with paying the extra amount."

If this happened to me, I would approach it from a sense of fairness. As in, it is not fair to me to pay that extra amount when I wasn't even aware that the session ran over, and even if I were, I was not aware there would be an extra charge. I am asking you to take that charge off my bill, and in the future, please stop our sessions at 45 minutes.

It doesn't have to take up your whole session. Your T is the professional, and as the professional, you have to explain your charges up front to people so they know what they are paying for. You just can't do your thing and then expect people to pay whatever amount you tell them to pay.

Edited to say: I see that I said the same thing as Murray, and probably others. Sorry to be redundant. Good point, Murray