Have you got security software installed - antivirus, anti spyware/malware etc?
Active X shouldn't affect your system in this way as it is a Microsoft IE browser technology only. But IE is deep rooted in the Windows OS. I would boot into safe mode remove the active X item if you can.
Then contact the bank for instructions as to sort out the problem. I'm not aware of any bank requiring this approach but every one is different - out of interest which bank is it?