The bell puzzle is a little strange in that it doesn't seem to grant a reward—other than your own sense of satisfaction at tidying up the bell tower. While you can play the bells after they are in place by shooting them with spells, there's no indication of what melody to follow, and players have tried a number of different ones to no avail. I think the simplest answer is likely that this is your reward; a giant bell-based xylophone that you can play songs on with your wand.
If that isn't enough for you, though, head to the top of the tower and you can find a legendary chest. If you jump into the frog statue that takes you to the next tower over, you can also grab some items for the Room of Requirement.