I think that common bribery situations in which tourists and residents of CIS countries may find themselves are very different. I guess tourists are more likely to be pressed for bribes by custom officers or by militia who insist on some imaginary passport regime violations. They act on the assumption that a tourist is not familiar with local laws and/or rich and/or scared of the bad CIS reputation and is an easy prey.

For a local resident, as it-ogo mentioned, bribes are usually used to cut the red tape and to save time, to gain some advantage (for example to enter the university when your grades are not so great), to avoid punishment or to get a better service. Nobody is usually actively pressed for a bribe in these situations (though some hints may be dropped), and it's often the bribe giver who initiates the exchange. If you don't want to give a bribe in 99% of situations you won't suffer any consequences, except that no one will fall over themselves to help you: you'll have to pay a fine, you deserve, everything you need will be done according to rules or law, which means an average or slightly below average service, a long wait, etc.