Is the amount paid to obtain a scholarship abroad considered a bribe, or is it in exchange for the efforts and follow-up to secure the scholarship? And is obtaining the scholarship in this manner considered acquiring something to which one is not entitled?

It is not permissible to travel for study in the lands of the disbelievers if beneficial knowledge can be acquired in Muslim lands. It is also not permissible to pay a bribe to obtain a scholarship, for the one who pays or receives a bribe is cursed. If obtaining the scholarship in this manner violates the regulations of the scholarships, then the prohibition is more emphatic. Added to this is traveling to the lands of disbelief without a legitimate Islamic reason, violating the terms and conditions, and taking what one has no right to.