With motorbike rentals, you should be a little bit careful. Most motorbikes have only comprehensive insurance. In case of an accident, this is very often not enough coverage and you might be fully responsible for the exceeding amount. Often you are responsible as well if the motorbike is stolen. Insist on a written contract and read it carefully before signing.
For tourists, a valid international driving license is accepted by the police. If the police stop you for driving without a driving license usually it is not that serious and will cost you a few hundred Baht. But in case of an accident without a valid International Driving license or a Thai Driving license, an insurance company may hold you fully liable and responsible for any accident and refuse to pay any insurance etc.
Foreigners living in Thailand permanently should apply for a Thai Driving License.