bridesmaid is a big commitment. it wasn’t fair for the mother to answer Yes. I also don’t like “being volunteered”. Usually I find ways to get out of it. But sometimes direct is the only way which is hard but not impossible.
Maybe go to the cousin directly and say something like, “I’ll be your bridesmaid if you like, but if you had anybody else in mind that would love to do it, I don’t mind letting them be bridesmaid instead. I hadn’t had time to process it really to be honest. What made you think of me for your bridesmaid? ”
Something like that maybe.
I would definitely try to skip over the mother’s head here. It’ll get back to her and she’ll be mad but I have a feeling that your friend will be able to handle that better than trying to go THROUGH the mother to get to the bride-to-be.
“Better to ask forgiveness than beg permission”.