How do I convince my girl to start riding?

People have, to a large extent, the ability to exercise freewill. If you're girlfirend wanted to ride a bike I'm sure she would be capable of communicating this fact to you, or whoever else she may feel comfortable discussing it with.

+1, if she can muster some enthusiasm for cycling then visit some bike shops together and let her tell you what kind of bike and riding (parks, pubs, commuting, training, track) she's interested in. Trying to manipulate her into being an unwilling fixie skidder is going to end in tears