What year are you in at university?
Your degree is finance-related, which is arguably a plus -- although the degree you do doesn't matter when applying to investment banking.
Aside from that, the usual route would be Spring Week in year 1 (of university) --> investment banking internship in summer of year 2 --> applications to graduate roles in investment banking in your final year.
The majority of graduate roles at the BBs will be filled by applicants who have interned there previously. They then open up to other applicants to fill up remaining vacancies. Because of this, it's often considered a prerequisite to intern in your penultimate year. That said, there are still many people who get in without internships (I know 2 such people personally), so there probably isn't any harm in giving it a shot if you're already in your final year. You might also have some other finance-related experience that you could potentially leverage towards getting into IB.