Yes indeed - you need work experience and lots of it. I don't mean to be cold, but I don't believe there is any b-school worth attending that would consider you at this stage. It is important to understand that MBA programs (at least those that are not 5-year BA/MBA combo programs) are not at all reset button programs or "first step" programs. Law school can be the first step towards a career in law. You go to law school, get a JD, pass the bar, become a lawyer. Med school is the same thing. Go to med school, get an MD, pass your boards, become a resident. The MBA is not like this. There is no licensing exam, no equivalent of a first year associate or resident. When you graduate with an MBA, the expectation is that you are ready to lead and work at a senior level. It is a midstream degree for that reason and to earn one before you are ready to make it pay off would be a disservice to you. Schools know that, so they won't even allow it to happen (not just out of the goodness of their hearts; they also don't want to take the hit in their employment #s).
If you want to get into an academic program, consider law school or a masters (finance, accounting, public policy, etc.). But an MBA is several years off.
Hope this helps you out!
Respectfully,
Paul Lanzillotti