I think we should be allowed to move the bank in our house/castle! It'd be a great addition. Whenever I want quick access to my bank, I always find myself unequipping my home so I'm teleported straight to the dorm where it is easier access, rather than using my beautiful house instead so I don't have to walk as far.
You can sort of do that now, though you have to "earn" the right to do it.
As part of the fall update, a new recipe vendor was added to castle tours and fully half of those recipes are bank boxes of various appearances. You buy the recipe, craft it, and drop it in your house wherever you want.
The catch is that you have to earn a badge to buy the recipe, and then earn ten "blueprints", which are a new reagent that comes from a new event called the Spiral Scene. It hasn't run on Live yet. On test realm, when it ran, it gave out ten blueprints which was exactly the amount needed to craft a bank box.
Watch for spiral scene, and in the meantime, rate a bunch of houses on castle tours to earn your Castle Auditor badge. (It takes 100 ratings, so ask yourself how badly you really want that mobile bank box.)