I'm quite possibly missing out on a lot, but I've never ridden a bike in Beijing. This may be a bit of a shame, but
I live so close to so much good public transport, I've never felt a need to. It certainly would be good exercise, but
between the sub-zero temperatures of winter, the humid heat of summer and the year-round pollution I'm not sure I need
exercise that much. If you want to, the cheapest, clunkiest bikes will set you back less than 100Y, and as is always the case, if you want to spend more there are plenty of people willing to take your money.
Roadside repairs are effected by people with toolkits who sit on street corners repairing bikes for ridiculously small quantities of money.