Hey there,
Yunnan is one of the best cycling destinations of China! But you should be reasonable fit to enjoy it, as it is mountainous almost everywhere. I wouldn't recommend cycling in the south in summer as it is simply too hot/humid (unless you can stand/enjoy this climate). The northeast is nice, with places like Dali, Shangri-la, Lijiang, and the Tiger Leaping Gorge, but the best about China is the possibility to discover places and meet people away from the usual tourist crowds. Yunnan is huge, so for just one month, you should consider using public transport once in a while. It is no problem taking bikes on local busses in China!
Enjoy!