I would like to rent a montain bike in Qingdao to sightseen the city ?Where can I rent the bike?

Actually, it is not suggested to bike in Qingdao, because the road is not flat. If you really want to rent a car, you can go to the Olympic Sailing Center, where you can find the bike on renting. You can take the bike to the hills outside the city. The rent fee depends on the time you rent.
As for your practising of the spinning, most of the gym provide that kind of service. Qingdao Beihai Gym is a good one for you, but I do not know whether it is close to your hotel or not.
I hope these information is useful for you and have a nice trip in Qingdao