Unless Cambodia has some agreement with Thailand, I can't see the difference of bringing a bike into Thailand from any other country, ie: Singapore, Malaysia, Australia. I got a 30 day customs "visa" regardless of my own visa status. Basically I had to get the bike over to a border crossing to the Thai customs every month. I even had a Carnet, which made no diffence.
I hope I am wrong in your case, it is always worth a try.
Cheers
Tom