Is presenting a valuable gift to the administration for approval of a master's research leave considered a bribe, and is this permissible?

The forbidden bribe is that which is given to invalidate a right or to establish a falsehood. As for what a person gives to attain their right or to avert injustice from themselves, it is not considered a forbidden bribe on the part of the giver. Rather, the sin lies with the one who takes it. The Prophet, peace and blessings be upon him, cursed the briber and the bribed. Therefore, if the administration unjustly withholds a student's right, and she cannot obtain it except by giving a gift, then there is no sin upon her. Rather, the sin lies with the oppressor who takes it.