Well I will add my experiences although with a car but in principle should be same.
First don't waste you time going to Buriram Transport office they do not issue vehicle passports.
I believe only provinces which border another country can issue them (they only last 1 year by the way) I have had them issued at Nong Khai and also Ubon Ratachani. For a car it is only 100 baht or so.
Regarding insurance immediately over the border in Laos anyway there has always been an insurance office which issues cover on the spot for a few days basic minimum cover at minimum cost.
Ah, also you cannot take a vehicle out of the country unless you own it outright. Don't forget to take the Registration book with you as they require sight of this.
You will also need to fill in a form to export the vehicle from Thailand and another to import to the country you are visiting. But a lot easier upon return.
Hope this helps