Giving a bribe is not allowed in Islam.
Following are the hadiths that prove it.
Dawud :: Book 19 : Hadith 2953
Mutayr said: I heard a man say: I heard the Apostle of Allah (peace_be_upon_him) in the Farewell Pilgrimage. He was commanding and prohibiting them (the people). He said: O Allah, did I give full information? They said: Yes. He said: When the Quraysh quarrel about the rule among themselves, and the presents become bribery, them leave them. The people were asked: Who was he (who narrated this tradition)? They said: This was Dhul-Zawa'id, a Companion of the Apostle of Allah (peace_be_upon_him).
Here the prophet says to not accept gifts given as bribes.
Another hadeeth -
Dawud :: Book 24 : Hadith 3573
Narrated Abdullah ibn Amr ibn al-'As:
The Apostle of Allah (peace_be_upon_him) cursed the one who bribes and the one who takes bribe.
When the prophet curses something then it has to be wrong.
Another hadeeth -
Malik :: Book 33 : Hadith 33.1.2
Malik related to me from Ibn Shihab from Sulayman ibn Yasar that the Messenger of Allah, may Allah bless him and grant him peace, used to send Abdullah ibn Rawaha to Khaybar, to assess the division of the fruit crop between him and the jews of Khaybar.
The jews collected for Abdullah pieces of their women's jewellery and said to him, "This is yours. Go light on us and don't be exact in the division!"
Abdullah ibn Rawaha said, "O tribe of jews! By Allah! You are among the most hateful to me of Allah's creation, but it does not prompt me to deal unjustly with you. What you have offered as a bribe is forbidden. We will not touch it." They said, "This is what supports the heavens and the earth." (this is not complete)
So these three hadiths say that giving a bribe is wrong.
Also in the quran it is given that bribery is not allowed
And do not consume one another's wealth unjustly or send it [in bribery] to the rulers in order that [they might aid] you [to] consume a portion of the wealth of the people in sin, while you know [it is unlawful]. [Surat Al-Baqarah 2:188] (Translation by Saheeh International)
And you see many of them (Jews) hurrying for sin and transgression, and eating illegal things [as bribes and Riba (usury), etc.]. Evil indeed is that which they have been doing. [Surat Al-Mā'idah 5:62] (Translation by Muhsin Khan)
O you who have believed, testimony [should be taken] among you when death approaches one of you at the time of bequest - [that of] two just men from among you or two others from outside if you are traveling through the land and the disaster of death should strike you. Detain them after the prayer and let them both swear by Allah if you doubt [their testimony, saying], "We will not exchange our oath for a price, even if he should be a near relative, and we will not withhold the testimony of Allah . Indeed, we would then be of the sinful." [Surat Al-Mā'idah 5:106] (Translation by Saheeh International)
And their taking of Riba (usury) though they were forbidden from taking it and their devouring of men's substance wrongfully (bribery, etc.). And We have prepared for the disbelievers among them a painful torment. [4:161] (Translation by Muhsin Khan)
Even these Quranic verses say that bribery is wrong.
May Allah guide you onto the right path.