Well, here's an idea: on the wave of all things bike now being "in", casually ask if she would come along to a bike shop to help you make up your mind on a new bike/tyres/whatever.
You will have to exchange numbers, so that's a start. After you go for coffee. Depending on how it all developed, a few days later you text her for something trivial, another few days later you propose something else, or maybe by that time she will want to take you to a garden centre

Whatever you do, do not propose a bike ride: unless she is a really good cyclist, and she knows it, she will decline for fear of not being able to keep up.
Good luck!