You will be doing both to get to/from your relief point, depending on where you have to go. Staten Island does reliefs outside the depots, so it's just a matter of going downstairs. But let's say Manhattanville or Quill for example, you will be taking the bus or train to your relief point.
If there's any new damage to the bus, it'll be obvious. The shop tends to smooth out prior damage, so you can tell the difference between the two, most of the time. So if it wasn't written up or can be explained, refuse the bus.