Q: How do I remove my bank details

On your computer's iTunes you should be able to edit your payment info by going into the Store > View Account menu option and logging into your account, and on your account's details page there should be a payment link.  If you are doing it on your phone then tap on your id in Settings > iTunes & App Store and tap on 'View Apple ID' on the popup and log into your account  - that should also give you a payments link on your account's page.

Changing payment info : http://support.apple.com/kb/HT1918

If you don't get the 'none' option on the payment details screen : http://support.apple.com/kb/TS5366