If you want to destroy a bank, do so by destroying the nation that surrounds it. Without the looted modifier, Braavos does not (at least, not for me) typically send faceless men. I mean, like, sometimes it does but no more often than anyone else rich whose land I raid.
Just keep on raiding them, especially when they go to war. Don't get too greedy; remember that ten smaller hauls tend to be safer and more profitable than one big haul and ultimately without the protection of the republic the Iron Bank will fall.
Really, the only time I could legitimately suggest looting the bank is if you have your own bank and are trying to take out the competition.
