From a hiring manager's perspective, these are the questions I will ask you
1) Why do you want to leave?
2) What knowledge do you currently have? I will also ask technical questions to verify if you indeed know what you claim to know, or you are just BS-ing.
How do I know that you are not going to leave, after 6 - 12 months, after learning sufficient knowledge to work independently?

Nobody is interested to spend time to train a junior, only to have the junior leaving, after learning the ropes. Its a complete waste of time, plus, most bigger banks have hiring restrictions. Resignation headcounts are not always replaced. And additional time to replace the headcount, or even losing a headcount will add unnecessarily stress to existing team. I have told HR to blacklist an employee, who joined the bank for a short period, and resigned shortly after, giving rubbish reasons during resignation. The market is small and the boy is only job hopping for more money. It is a complete waste of my time, and I do not want the same person to waste my colleagues' time.

If you feel that you can take on more responsibilities, you should step up and talk to your direct supervisors. You should not worry about annoying your peers/colleagues. At the end of the day, you are responsible for planning your own career path, not theirs. If they decides to not take any action, they have themselves to blame. If you can't even manage your peers, how do you expect to manage them, if you become a supervisor one day?

You should also bear in mind, most supervisors will only consider putting a candidate for a promotion, after the person has proven over 2 consecutive years outstanding performance. There are always exceptions, but they are exceptions.