It's definitely an attack and you'd be wise to not enter any details (as you've already noticed). Most people are oblivious to this sort of attack so kudo's on your part. If you have windows 7 or earlier operating system run this http://www.bleepingcomputer.com/combofix/how-to-use-combofix
If you have windows 8 however, we'll have to find a different tool as this doesn't work with windows 8 yet I don't believe. This has been my goto malware removal tool for quite a while, it's excellent, far better than anything else I've ever used. It can take 5-15 minutes to run though so if it's taking it's sweet time, be patient. The attack may not be on your machine though as smc mentioned. It's considered a man in the middle attack which in this case is redirecting you to a fake site in an attempt to get your cc info. If it finds nothing, it's still possible there's something on your machine that combofix hasn't learned to detect yet but I doubt that'd be the case. More likely a machine between you and the bank is compromised and contacting your isp would be the next step for me.
It also sorta sounded like you were using random public wifi to get online. Maybe the person you're connected to is infected (or purposely being the attacker -- which in my view you deserve for stealing wifi!)
