Hello all (and Merry Christmas), I am new to these boards, but I would like to hear some opinions about the situation I am in.

I am 20 years old and a senior at the University of North Florida, 2 semesters away from earning my bachelors degree in Health Administration. I am also an assistant manager at a dessert place in Jacksonville, Florida and handle inventories, nightly banking, and other financial/managerial aspects such as scheduling, paychecks, hiring/firing, and overlooking other employees as they are working.

I am planning to do my Health Administration internship this summer (and graduate right after), and I was originally planning on being in a MSP/MBA dual degree online program from UF and Stetson University, as I want to pursue a career in pharmaceutical business.

However, I am unsure about whether this is the right route to take. I am aware that many MBA programs and many professional jobs require 2+ years of professional experience. Though I am an assistant manager at my job and deal with a lot of major business aspects, I am not sure if this is considered "professional experience" as I am managing a restaurant, and not a hospital or a major organization.

Should I wait a few years after obtaining my bachelor's degree to try to get into the MBA/MSP program (or any other MBA program)? Do you think my experience managing this dessert place will be enough to relate to material discussed in MBA classes?

Your current management experience sounds great. I'd encourage you to think about why you want to pursue graduate school. Would it simply be to garner advanced degrees? Would it be to enhance your managerial skills? These are the types of questions that business schools will likely want to know the answer to. Such questions are asked via essay prompts such as "Why do you want to attend X school of business and how do you see an MBA helping you achieve your professional goals? Don't worry about experience or age. Focus on your mission and purpose. Note that some schools welcome early career MBA's.
http://www.princetonreview.com/early-career-MBA.aspx

It is not impossible, but statistically speaking, your chances of getting into a good school are higher with a few years of work experience after undergrad. You will also find your MBA experience much more satisfying because you will be able to relate many of the concepts to your work.

Having said that, the youngest guy in my class at Wharton was only 18 when we started the program in 2008.
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