I doubt that OP would qualify for any reputable EMBA (Executive MBA) Program without substantial (typically 10 years including at least 5 years of management experience) work experience. However, much is changing in the MBA field so these guidelines may change.
Currently, several MBA programs are not requiring standardized test scores–even though the GMAT is readily available on demand during regular testing center hours.
Some programs are investigating whether or not the GMAT / GRE should be a requirement for all applicants. For example, those who have earned CPA licenses, law degrees (JD), or have in excess of 5 years of work experience may be able to apply without a standardized test score at some MBA programs.
OP: If you deal directly with the IPO folks (investment bankers, lawyers, & accountants) , you should earn an informal mini-MBA.
P.S. Another option is to enroll in an online or hybrid MBA program which should not disrupt your full-time work after completing your undergraduate degree.