I just came back from China, spent 1 month in Shunde (south, close to Hong Kong)
Not many bike stores, especially near my hotel and work, but I've managed to find some and took a look
ended up buying a bike (sunpeed brand), a bike bag, and traveled back with a new toy lol
if you want to buy a new bike, I'd say that buying a frame and building a new one would be really hard. But you can find some bike store in your area and get some good deals
especially chinese brands, I went with Sunpeed which was the cheaper, but I saw Winspace there too, a brand called Camp, also Pardus which is a bit more known, and XDS which is a big chinese manufacturer and has a lot of good deals too (but the store didn't help much, otherwise I'd have bought there)
anyway, in Shanghai you'll probably have more options, I'd recommend searching Amaps or Baidu Maps and seeing what stores there are which are easy for you to get to