It depends on what you do at the bank. If it is considered a skilled job, then you have the opportunity to ask the employer to sponsor you through a provincial nominee program or you could work for 2 years and apply yourself under CEC.
You can see some different bank titles here: http://www5.hrsdc.gc.ca/NOC/English/NOC/2006/SearchKeywordResult.aspx?val11=bank&val12=0&val13=0&val14=blood&val15=1&val16=0
The ones where the 4 digit code starts with 0, 11 or 12 are skilled. The ones that start with 14 are not.
If your job is not skilled, you have no options for immigration in a bank. A couple of provinces have special programs for employers to sponsor low skilled workers in certain fields like tourism and production, not banks. It would be better for you to get a skilled job.
If you are not skilled and can not get promoted at this bank, look for something else that is skilled. You can look for titles at the website above. All jobs where the first digit is 0 are skilled and if the first digit is not 0, you look at the 2nd digit and that should be 1,2 or 3 for it to be skilled.
