If you try to purchase items from a vendor that cost a Warbound item and you only have the item(s) in your Warband Bank, (for example, buying Pet Battle Training Stones with Polished Pet Charms) it will say “You do not have the required items for that purchase”. You then have to go to the Warband Bank and withdraw those items to make the purchase. This also occurs with things like cosmetic weapons from Dragonflight Renown vendors.
I hope this is a bug and not intended because for how much gold it costs to buy the tabs, that would be a terrible limitation that would make the Warband Banks significantly less useful and be akin to just a guild bank.
The reasons I think this is a bug though are 1: you can make purchases like this if those items are in your regular bank, and 2: the currency items will show in full color as the price when the items are in your Warband Bank and not be grayed out like they usually are when you don’t have sufficient items to make the purchase.