Each BOD type will have a greater chance to change one of the properties one step, compared to the other two - unless in case you need that step, in which case it's like it can read your mind, and it will buck the chances and go for one of the rarer upgrades...
At least, that's how it seems sometimes.
Also, the price changes with each BOD bribed at that specific NPC, and after a random number of bribes, they will claim they're afraid of being caught, and won't make an exchange until they cool down.
The secret to cheap bribes is to look for places not many people frequent, and the bod-givers there. For example, some Ilshenar NPCs give BODs/do Bribes. Some cities in Fel are rarely visited on many shards, because they aren't part of VvV or can't be gotten there easily. And some in both Tram & Fel aren't on the Moongate system.