I have been in banking for 15 years and have never disqualified someone on a poor credit score alone. You may want to check with the bank and see if they refused to open your account due to a poor chexsystems report. This tells the financial institution if you owe money to other banks or if you have been flagged for account abuse.
You can get a free copy of your report at www.chexsystems.com. You are also entitled to get a copy from a bank that denied opening an account for you. Also don't be afraid to ask the manager for help understanding and/or correcting issues. Most managers are very nice and willing to go over it with you.
As far as increasing your credit score you may want to use Credit Karma. They will show you your credit reports and give you tips on how to improve your credit. Just keep in mind that their score is not a FICO score so it's not completely accurate but it does give you a good ball park.
Best of luck to you!!
