Need advice in regards to applying for an MBA program with military experience

Hey everyone. I've been searching for awhile now and can't find the specific answers I'm looking for so figured I'd post here. After previously serving seven years in the military (special operations, for context) I am finally graduating with a BS in finance next month from a somewhat semi-target university. After a few internships and heavy networking, I was able to secure a solid job in corporate banking at a BB post graduation. Here is where my head is at right now and also where I could use some advice. Given the fact that I'm sort of behind the curve at 30 years old and just now finishing undergrad due to my time in the military, would it be worth it for me to apply for business schools (part-time/weekend programs while working) right out the gate?

I know I know.... que the "you need work experience in order to apply" part of the responses I'll get. After speaking to a few admissions counselors, I've found that grad programs gladly accept military experience in lieu of "traditional" business experience so that's not the issue. My question is will it be worth it for me to pursue this option part time right away, given the fact that my peers have a head start on me having already been working for the past 6-7 years? I understand the value of having that business experience going into grad programs, however I'd rather not wait until I'm 35 to then attend b-school.

I'd appreciate any thoughts, comments, and/or recommendations. Thanks!