I'm thinking you should maybe go easy on talking about the different goals and different speeds etc you have if she's competitive, and just try bringing up how you really enjoy riding on your own. If she has kids too that may help her understand. I'm known as that much of a loner that if someone asks "hey, shall we do this or that together?" I can say "sorry, not today, I need/want to ride on my own today, how about Thursday", and then I can make Thursday the social occasion. It's not about being anti-social or not liking her company, just enjoying all of other things that go with doing things on your own, freedom, concentration, time to focus and think, being free to get really cranky or upset without bothering anyone else

Funny, I have the feeling men don't have to have these conversations that much. There isn't really any reason you should have to defend wanting to do something on your own instead of with a group of people.