Dear Eyvor,
Thanks for contacting Top China Travel!
There are some bike rental stores in Shanghai. But I am not sure the exact rental sites of them. I heard that you can easily find them in the nearby area of famous universities in Shanghai, such as Shanghai Jiaotong University, East China Normal University, Shanghai International Studies University, etc. You can easily to find a place to rent bike around these university. You can ask the local people when you get there.
Any further request or question, please feel free to contact with us.