What is the ruling on my remaining in my current job until the end of my contract, or tendering my resignation now, or changing my job title and remaining with the same company, knowing that the nature of my work requires me to deal with bribes, and that most of the company's projects are carried out through bribery?

Bribery is forbidden if it is given to nullify a right or to uphold falsehood. However, what is given to ward off injustice or harm, or to attain a right that is otherwise unattainable, is permissible. So, if competition cannot be won except through bribery, and you are the rightful party, then it is permissible to give it, and the sin falls upon the receiver. As for scheming to eliminate competitors, that is not permissible. It is not permissible to continue in a job if it involves direct involvement or assistance in forbidden bribery and scheming. Otherwise, it is permissible to remain in it while abstaining from engaging in forbidden practices.