I would think that the bigger issue is that you are already a general manager... from the ad com's perspective, you've already achieved your goal, and don't need business school! You probably should reposition/reframe your goal to be more specific. I'm not sure what industry you're in now, but chances are that you could apply to a general management role in another industry and get the job.
I would make your long term goal more ambitious, and then identify the skills that you are missing to be qualified for that long term goal. Then, choose a short term career that would help you build those skills (whether that's industry knowledge or functional knowledge or leadership experience or large company experience, or whatever).
I hope this isn't too vague - feel free to ask any clarifying questions!
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