I want to buy a ordinary bike to go bike riding but I am short?

Depending on the type of bike you will purchase you need from 1" to 3" of clearance between the top tube and your groin. If you are 5'1" a 60c bike is waaaay too large. You are looking in the 48-52c range if that helps. This is only a generalization. You will still need to be fit to a bike at your local bike shop. It's all done as a pre-purchase test fit arrangement so there's no obligation, and there's no way to get around it, unless you have some experience at buying a bike for yourself.
 
Visit the local bike shop and get fitted, it will depend on the type of bike you want to get.

http://www.coloradocyclist.com/bikefit/
 
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