You can buy a motorcycle.. but renting, I can’t imagine ANYONE renting a motorcycle to someone, especially without a valid motorcycle driver’s license. Their name is strapped to the vehicle – here, fines/problems go directly to the owner of the vehicle rather than the driver. If you’re screaming through red lights or speed traps, it’s all on them – absolutely not worth the risk for any potential renters.
You can buy a motorbike pretty cheap online. It wouldn’t be in your name, so if you’re busted, while you should get the little blue book etc, it may be a challenge to get it out of the ‘impound’ equivalent..but foreigners I know who have owned bikes never got put into that predicament.
It’s not like Thailand, Vietnam, most other countries – where international licenses are recognized and scooters/small bikes are easy to rent..but that being said, a few thousand RMB on taobao and you’re good to go if you’re willing to consider it semi-disposable 😀