Can I port my bank health insurance policy?

As per IRDA policy of any company purchased thru a bank or a corporate cannot be port to any other company. To buy a policy of any other company you have to buy a fresh policy with all the waiting period and other clauses.
You can transfer your policy from bank to same company directly at actual premiums. In such case your same policy will continue. As a bank health policy has lots of issues such as no additional features and risk of tie up breaking. So it better to use a backup policy along with your exiting bank policy.