First of all, bribing an official in Thailand is illigal. This is prohibited by law.
We can only talk about an expression of honor and respect when dealing with a police officer to save his time doing paper work when you brake some minor road traffic rules.
Most traffic fines are between 200 and 1000 baht. The ligal thing to do is to take a ticket and go pay it at a police station and lose some of your time feeding bureaucratic machine.
On the other hand you can save officers’s preciouse time from filling in documents. Just say “No receipt required, officer” and pay your fine on the spot.
If by the time you read this article this way of paying road fines would be illigal, please don’t do it, ok? 😉