Public Bus System 公交系统
In Shanghai public buses cost 1 yuan per trip for normal buses and 2 yuan per trip for the air-conditioned buses.
The public bus system is quite extensive, but the signs at bus stops are usually only labeled in Chinese.  If you know Chinese or can get somebody to help you pick your route, the bus can be more convenient than the subway and cheaper than a cab.
For more info (in Chinese only) try checking the official website for transportation in Shanghai.