I know it uses wizards tokens so im saving them up, but when does it restock?

I believe it's entirely random, which makes it all the more difficult to get an item from there.

It restocks when it damn well pleases XD

But really, it's random and supposed to be somewhat infrequent.

Also note that not everything from the BHH is worth its price in Wizard Tokens; some for less than the tokens themselves as a result of restocking there for so long. I'm just adding this in case you assume that just because the BHH restocks rarely, doesn't mean everything in there is worth a ton. :P