Yeah, bribes are just the cost of being a foreigner in many parts of the world, and they're often not too bad (unless you did something terrible).

Before visiting a poor country, figure out how much a bribe should be and consider it similar to a tip here. Policemen aren't paid very well, so it's kind of like tipping an underpaid waitress here in the US. Account for it as part of your overall expenses and you'll be fine.