Is it permissible to work for a private institution that engages in the following practices: submitting bids in the names of other companies to increase the chances of winning tenders, taking interest-based loans, and paying bribes to government officials?

It is not permissible for an establishment to submit a bid on behalf of another establishment due to the deception and fraud involved. You are not allowed to do this work; rather, you should limit yourself to writing only your own establishment's bid. If the establishment borrows with interest (riba), the sin is upon its owner and whoever directly engages in this borrowing or assists in it through recording and documentation. If your work is far removed from that, then there is no blame upon you, for it is permissible for a person to perform a permissible job for someone who deals with riba. If the owner of the establishment pays bribes to some government officials overseeing those tenders, and you have no involvement in that, then there is no blame upon you. You are permitted to work in this establishment as long as you do not directly engage in any unlawful acts within it, nor assist in them.