'Hi W, I would like see if I can swap weekends with you for X and X, as long as you don't already have plans. Thanks, and let me know when you can'.
I wouldn't tell her what's going on unless she asks. If she does, keep it short and sweet. 'There's a bike race I'd like to race in, but if it doesn't work for you that's okay'. Don't indicate that you really want to do this, or she may fight you on it just to be difficult.
