This isn't something you'd need to do in most countries - you'd simply apply for a scholarship, loan, or grant from the government or the school directly.
But here's an example of the kind of letter you could send to the bank to explain the financial help you need:
To the Bank Manager,
Bank Name,
City Name.
Dear Sir,
SUBJCT: Requesting education loan.
I am planning to study (name of course) during the years (2013-106)
Please grant me a loan so that I can pursue my education. I've inclosed the copies of my relevant study documents.
Enclosure :
1. Mark sheet of previous semesters.
2. Bonafide certificate.
3. College letter.
Yours sincerely,
(Your Name)
Use this as a basic guide and customize it to meet your requirements and you should do fine.
Good luck!