If Bud were growing up in an orphanage today, I would hope that the revitalized system, so different than the one so overrun during the Depression would try to find Bud's relatives for him instead of him having to look for them himself. Though no system is perfect, I would also hope that they would make a better job of finding a good fit for Bud in foster care. Of course, across the board, orphanages are probably struggling today as well, but with computerization and better education, as well as a society that supports children (or should) of all color, race, culture, etc., I would like to believe that Bud's experiences from the time he was small and lost his mother would have been more nuturing and protective of him.
Running away would not have been so easy, but in this story, it is only his ability to leave the system that allows him to meet new people, learn about the world and ultimately find Herman E. Calloway, as well as a new life.
Today there are very few places one would call orphanages. Instead the system relies on foster homes and some group homes. Bud would have his life be limited. He would not be able to take off and go over the road to find his father. He would be found quickly and returned to where he lives. If he tried to run again the authorities would have put him in a more restrictive facility.
The people around him would be nice and they would get money for caring for him. Depending on who is raising him, he would either have nice clothes or second hand clothing. He would be safe though because the state would protect him by sending social workers to check up on him. He definitely would not have any of the freedom that he took when he set off to find his dad. He would still miss his mother very much.