PvP skins actually go into your PvP Locker.
You can access this by hitting the little crossed-swords icon at the upper-left of the screen to Enter the Mists, the sPvP staging area. Here, vendors to help you swap out your PvP gear and the like exist as well as tutorial NPCs. In any case, the lockers are in a row against a wall in this area, usually back and to your right as you zone into it.
If you’ve never been there before, you will first start out in a tutorial area and need to move forward to get to the main staging area.
Another thing to note is that this locker cannot hold stacks. So if you have, say, the PvP Forge Dagger stored away already and get another one, you cannot deposit the second one unless you take out the first one and equip it on a character, for example.
This locker only stores PvP weapon and armor skins. All of your crafting materials, foods, minis, and such are stored in the bank collectibles tab.
edit: Ah, took too long to post.
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