I like to work out alone also, but sometimes working out with others helps motivate you more! I recently joined the YMCA, and I am nervous working out in front of so many people..but then I think..they are there for the same thing! Why should I feel embarrassed? Just go with the flow, worry about your own self.
Easier said than done, but..still. heh.
If you feel the need to exercise alone, then just tell her in the nicest way possible. Tell her you do better by yourself, and that it's not that you don't want to spend that time with her...it's just something you have to do alone. If she is an understanding person..well..she should understand.