Here's the deal,
Okay, I bought an iPhone 6s on friday, I had no issue adding my cards, it was on iOS 9.0, now, I updated to 9.0.1 after setting everything up, and the card issues began, as I had to to an erase all settings due to the transfer from my icloud back up as there's an App Slicing bug, so I decided to reinstall everything from the app store from scratch, this was when i could not re-add my card after the reset/erase, so having spent over 6 hours on the phone to halifax and apple, who blamed each other, I was finally advised to return the phone to the store, so, I got a brand new sealed iphone 6, and the card added no problem, in iOS 9.0 again, so I then decided, to upgrade again to iOS 9.0.1, once more the issue returned, so the issue is caused by iOS 9.0.1, so until they fix the issue, you can either...wait for 9.0.2, or order a replacement bank card, as the 16 digit number will have changed the card will add no problem, it seems to only occur with Halifax / Lloyds VISA DEBIT cards, as my credit cards re-add without issue. I have tried to downgrade back to iOS 9.0, but it does not allow, I have also reformatted via the phone, via itunes, restored for a back up, set up as new, and as soon as you have iOS 9.0.1 installed you hit problems.
Reading up further the issue also occured in iOS 8.1.2, and was fixed without an update, so maybe there's something in the iOS that the servers don't like, maybe it's possible they can iron it out on the server end without an update.
You may also notice that some apps will no pass the splash screen when setting up from an iCloud back up on the 6s, if this happens just reinstall that app from the app store, it's an App Slicing bug.
http://www.forbes.com/sites/gordonkelly/2015/09/27/apple-ios-9-third-problem/