Hi Mach, welcome to the forum. Sorry to hear about your accident with the bus. You are well entitled to make a claim for compensation, you don't have to do it through the bus company because you can make the claim yourself through a solicitor. You would need to give the solicitor the details of the bus company/route number & area etc as well as the details for the car driver.
If you don't have the drivers details you may want to give the bus company a ring, explain what happened and ask for the registration number of both the bus and the car and then you should be good to go.