Usually the announcement is not "we have stopped at Foo and Main". The announcement is "Next stop Foo and Main" while you're on the way to it, so you have time to sling your bag back over your shoulder, get your coat back on, and make your way towards the door. Depending on the density of stops along the route this can come anywhere from 1-7 blocks ahead of the stop.

Source: I don't drive,and ride the bus a lot.