How would I draw to a mutable in-memory bitmap?

Question

I'm trying to write a simple painting app for iOS as a first non-trivial project. Basically, on every touch event, I need to open a graphics context on the bitmap, draw something over top of where the user left off, and close it.

UIImage is immutable, so it's not exactly suitable for my purposes; I'd have to build a new bitmap and draw the old one into the new one. I can't imagine that performing well. Is there any sort of mutable bitmap class in UIKit, or am I going to have to go down to CGImageRef?