Firstly: 

Wasaatah (intervention) means intercession, and intercession may be good or bad. The good type is that which helps in good things and serves to attain that which is permissible, without transgressing against the rights of others or giving precedence to one who does not deserve precedence. 

The bad type is that which helps in evil things, or is a means of wrongdoing, and giving preference to those who do not deserve it. This may be done with or without paying a bribe to the intermediary. 

Please see question no. 26801. 

Bribery means giving money to someone through whom a person takes something that has no right to, such as bribing a judge to judge in his favour wrongfully, or bribing an official to give him preference over others, or to give him something to which he is not entitled. 

Bribery is a major sin, because the Prophet (peace and blessings of Allaah be upon him) said: “May the curse of Allaah be upon the one who pays a bribe and the one who takes it.” 

Narrated by Ibn Maajah (2313); classed as saheeh by al-Albaani in Saheeh Ibn Maajah. 

See also question no. 22452 and 70367 

Secondly:  

It is permissible to pay a bribe if a person cannot attain his rights in any other way. But in that case it is haraam for the one who takes it but not the one who gives it. 

Ibn Hazm (may Allaah have mercy on him) said: Bribes are not permissible. A bribe is what a man gives so that a judgement will be passed in his favour unjustly, or so that he will be appointed to a position of authority, or so that a person will be mistreated for him. This is a sin for the one who gives it and the one who takes it. 

But if a person has been deprived of his rights and he gives a bribe so as to ward off mistreatment from himself, this is permissible for the one who gives it but it is a sin for the one who takes it. End quote from al-Muhalla (8/118). 

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: If he gives him a gift so that he will refrain from wronging him or so that he will give him his rights, this gift is haraam for the one who takes it, but it is permissible for the giver to give it to him, as the Prophet (peace and blessings of Allaah be upon him) said: “I give a gift to one of them and he will depart, carrying it under his armpit like fire.” It was said: O Messenger of Allaah, why do you give them gifts? He said: “They insist on asking and Allaah insists that I should not be stingy.” Giving to these people is permissible for the giver, but it is haraam for the taker to take it. 

With regard to giving a gift in the case of intercession, such as if a man intercedes for someone with a person who is in authority in order to relieve him of wrongdoing or to help him get his rights, or to help him get a position for which he is qualified, or to help him enlist in the army when he is qualified for that, or to get him some money that is given as a waqf for the poor, fuqaha’, Qur’aan readers or worshippers, and he is entitled to it, and other kinds of intercession which help in doing an obligatory action or avoiding a haraam deed – in these cases too it is not permissible to accept a gift, but it is permissible for the  giver to give that which will help him to attain his rights or ward off mistreatment. This is what is narrated from the salaf and the greatest imams. End quote from al-Fataawa al-Kubra (4/174). 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: As for bribes by means of which a person attains his rights, such as when he cannot attain his rights except by paying some money, this is haraam for the one who takes it but it is not haraam for the one who gives it, because the giver is only giving it in order to get his rights, but the taker who takes the bribe is sinning because he has taken something that he does not deserve. End quote from Fataawa Islamiyyah (4/302). 

And Allaah knows best.