Hi Commuter, I'm affraid Shanghai is not a good city for bikes. Getting a license is the first headache, I finally got one after being in China for 5 years. In Shanghai the only big bike available is the Chang Jiang, and they are crap. They have their following especially amongst the big German expat community, but they are hard work to say the least.
One bright light is that you can buy 125cc Sachs Mad Ass' and although small they are a hoot in Shanghai.
Traffic is bad, driving quality terrible.
There is a big bike club called the red devils I think, google it.. they will tell you some stories of how members bikes arrived in China, basically all different with varying degrees of legality and difficulty.
many cities have banned bikes completely, many of Shanghai's roads are off limits to bikes. All highways are a no no...
So not very good news.
If you were in the countryside it would be possible, but again only small bikes.
good luck.