Physics and SEPTA

To the left is a system schema of you and everything you're directly interacting with during this scenario. Under it the the free body diagram which shows you the forces that are present in the scenaria.

 

Fn represents Normal force, Fg represents gravity, and Facceleration is the push you feel when the bus accelerates. As you can see, the acceleration is greater than friction. If friction was equal or greater than the acceleration, you would not move at all.

 

When there is water on the floor, there is simply less friction.