2 bedroom apartment and general cost of living?

It's difficult to answer unless you provide us with some more details. Shanghai in typically a city were you can find everything in every price range, it all depends on your standards.

If you want to live in a well maintained, modern compound i'd say a basic two bedroom may start at 6000 rmb. You can get cheaper, but there's a chance it will be in half rundown buildings without elevator. At the same time you have a lot of more expensive options in fancy nancy compounds (up to several tens of thousands rmb a month).

About food and transportation, it might be good to know that Shanghai is never listed in the top of worldwide cost-of-living surveys over the last few years. If you google a bit, you can easily find these surveys online and check where shanghai is situated compared to your home city.
Transportation is considered cheap here (especially subway) and food can be cheap too, just depends on your lifestyle.