Bribery is haram in Islam, the one who gives and the one who takes, both will be the fuel of hell (Jahanum). But nowadays there are times when we have to pay up something to get our right, but will it be considered haram? No, it won't be.
If you pay up bribe for refraining someone else from their right and to possess something that you don't deserve legally, then it's haram, because you did take someone else's right by force. But if a person can't get his right except by paying bribe, then the scholars agree that it is permissible for him to give the bribe, and still the one who'll take it will be cursed (as it's haram for him to take bribe). For example: if you pay some money to a judge to show favor in your case, even if you don't legally deserve the favor, then it's haram. But if someone is obliged to save his/her respect from a poet or media, and then he/she pays up something to keep them silent, then it won't be haram for him/her but for the one who will take the money.
Indeed we all should know that Islam isn't a cage, it got limits, but it also got exceptions, Allah didn't order anything to put us in trouble, indeed all of it is for our own ease. Peace!
