I'm starting from the assumption that one is not allowed to catch a bus on shabbes, but would like to know why. Excluding issues pertaining to the purchase of tickets or the use of passes, potentially tangential problems such as carrying tickets or money where there is no eruv, and the avoidable problem of pushing the button to indicate where you wish to get off, what are the problems with riding on the bus?
Is it simply a case of mar'is ayin? Is it because my added weight (however infinitesimally) increases the payload of the vehicle and causes it to burn more petrol? Or are there other reasons as well?
For the sake of an argument, I am assuming that the driver is not Jewish, and that neither are (at least some of) the other passengers.