Apparently not since there are no viruses that affect or infect iOS.
How would this Einstein at your bank know your iPhone has a virus, which means you downloaded and installed it from an email attachment or from a website which is impossible with an iPhone - unless you have hacked your iPhone with the cutsie term for that - jailbreak. Have you hacked your iPhone? The definition of a virus includes the ability to spread from computer or device virally - without the infected users knowledge. If a virus, this means it has spread from your iPhone to other iOS devices virally, which is impossible with a non-hacked iPhone.
And before the iPhone, you never did online banking with this bank?
If your secure bank has an iPhone app, probably a good idea to use it, but I world run from that bank in a hurry.