Years ago we had a long discussion about sharing recipes. It was an eye-opener for me. I figured sharing was normal, but I came to understand that some people prefer not to share, especially when they have put a lot of time and energy into creating a recipe.
In answer to your question, no, I don't think you were rude to ask, but I don't think she was rude to refuse, either. It sounds like she was abrupt with her response, and it's rarely fun to be on the receiving end of an abrupt response. But yes, there are definitely people who don't share recipes. I've learned to ask, "Do you share your recipe?" rather than "Can I have that recipe?"