[It is permissible for the rightful owner to give a bribe in order to obtain his right(1)]

Answer – and Allah is the One who grants success: The scholars of the madhhab have forbidden that, as is stated in the marginal notes on al-Bayān. However, Imām al-Manṣūr Billāh, Imām Yaḥyā ibn Ḥamzah (Peace be upon them), and others allowed it.
What appears to me – and Allah knows best – is that if the rightful owner knows that he cannot reach his right except through a bribe, then it is permissible in that case; and that is for two reasons:
1. That His saying, the Exalted: “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].” [Al-Baqarah:188] does not apply to the one we have mentioned. Rather, it concerns those who bribe the judges in order to consume people’s wealth without right, whereas the person in question is merely ransoming his own wealth, not the wealth of other people.
2. Analogy with the prisoner of war: it has been established that it is permissible for him to ransom himself from the oppressor with his own wealth.
If it is said: It has come in the ḥadīth that the one who gives the bribe and the one who takes it are cursed.
We say: That is general, and it can be specified by the implied meaning (mafhum) of the verse and by analogy.
Furthermore, we do not concede that the one we have mentioned is called “a briber (rāshī)”; perhaps this name is specific to the one mentioned in the verse.
Moreover, what we have mentioned can also be supported by the fact that Allah, Exalted is He, has forbidden squandering wealth, and He has permitted for the one in dire necessity what is not permitted for others.
It may also be inferred for what we have said that it has been narrated that the Prophet (May Allah bless him and his family and grant them peace) considered giving the polytheists, during the Battle of the Trench, some of the fruits of Madinah so that they would turn back from the Muslims in that expedition; and he gave those whose hearts were to be reconciled (al-muʾallafah qulūbuhum) among the polytheists on the Day of Ḥunayn, in order to incline them towards Islam and to repel thereby their harm. And Allah, Exalted is He, has assigned them a share in the zakāh in His Noble Book.
Thus, the utmost that is in the matter is that it is not permissible for the judge to take wealth in order to judge according to the truth; for it has been established that it is not permissible to take a wage for an obligatory duty, as in His saying, Exalted is He: “And they were not commanded except to worship Allah, [being] sincere to Him in religion, inclining to truth, and to establish prayer and to give zakāh. And that is the correct religion.” [Al-Bayyinah:5] and His saying, Exalted is He: “Say, ‘I am only a man like you, to whom has been revealed that your god is one God. So whoever would hope for the meeting with his Lord – let him do righteous work and not associate in the worship of his Lord anyone.’” [Al-Kahf:110].

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2