I don't think it's rude to ask. It's up to your T to tell you yes or no, but you can always ask.

In my case, I don't have insurance that my T accepts now, so I asked her if she could give me a reduced rate. I think her answer was that she could, but it would have to be twice a month instead of weekly. I didn't dare ask if I could see her weekly at that rate. She said it would be for 60 minutes, not 90, or maybe I suggested that. She's doing me a big favor and said that it's all right, but I can't ask for anything more.