Out of the bank - you don't say "out from the bank" I'm pretty sure. "From the bank" means that we walk away from the bank building or there are 3 miles from the bank to the next street...
I agree with you. I added it as accepted translation.
Would the sentence mean the same if it just said sétálok instead of besétálok?
Magyars love the verbal prefix. If you say "sétálok a kórházba" insted of "besétálok a kórházba", then it means slightly different: you are somewhere else, so you're walking towards the hospital.
This is the true reality :))