I'm not sure if you can, check Claptraps house, there is a bank and the shared stash in it. I don't know if its only available on your second playthrough or not. --- You'll get no signature from me until GameFaqs is troll free!
Wanted to use this chararter as a storage character using the infinite bank space glitch....right now my lvl 50 gaige is using this glitch but in fear of it being patched and loosing her save altogether i wanted to move everything to this low lvl charcter. I would need to be able to access the seceret stash and bank quickly