www.annualcreditreport.com is the only authorized web site to get a credit report from all three bureaus, once per year free from each of the 3 main credit reporting bureaus.
Each credit reporting bureau also has a subscription service that allows you to get your credit report as often as you want. You might investigate to see if they have a free trial period that would let you get a report, or you could sign up for one month, get your reports, then cancel.
I'm puzzled by the idea that there is not enough info to provide a report -- if one bureau has your info, then all three should, unless for some reason all your credit cards only report to one of the bureaus. Or maybe there is confusion between you and someone with a similar name. You may need to call their customer service and talk to someone about your report.
I'm also puzzled as to why the bank doesnt get them themselves and wants you to do it. Cheesy cheap bank.