The first step is looking at what actually caused your injury. There can be a multitude of factors but usually there is one or two primary reasons for an accident. If the injury was caused by a defect with the vehicle or tracks itself, or by the actions of anyone working for the transportation agency (e.g. an operator, driver, dispatcher, maintenance person, etc.), then there is a high likelihood of recovery. For example, if your bus driver negligently drives the bus into an accident, causing your injury, then you will have a strong case for recovery against the transportation agency.
Even where the accident was not directly caused by the transportation agency, you may still have a valid claim. If there was a dangerous condition that caused your injury that the transportation agency should have remedied but did not – for example, if a rider dropped oil all over a platform, no one cleaned it up for hours, and you slipped on it – then you could have a valid claim. Even if someone commits a crime against you on public transportation, you may have a claim if the agency was negligent in maintaining security.