Welcome to GMAT Club!
I'm in a slightly different position as I will be completing a PT program while staying with my Big 4. Perhaps my responses will still hold some value for you:
1) How long? I'm a Senior 3, so coming up on 5 years with the firm. I expect to be promoted to manager this year. I think anytime from Senior 1 on is acceptable for U.S. MBA programs- with that one year of review/staff management experience you'll have better insight for essay/interview answers as well as a much better grasp of how our clients operate.
2) Why an MBA? I work in a niche consulting practice, not in a traditional tax/audit role, and many of my colleagues are now being hired from law school and PhD programs. I was an undergrad campus hire. While not required for me, per se (I have a non-CPA certification that is relevant in my field) I do feel the need to further my education to remain competitive and on the partner track, which is my goal for now. I always did expect to continue my education to the master's level. Also, I have a strong desire to teach in the future and a brand name MBA (I will be attending Chicago Booth this fall) should help to open doors when I want to make that jump in the future.
3) Experience/skills? Everything!

Big 4 has a lot of excellent connotations for grad school applications, namely good work ethic, relevant professional experience, good understanding of accounting (obviously). I, too, was surprised to not find more MBA applicants from the vast Big 4 ranks. However, I think a lot of B4 employees these days have already done a master's of accounting just to qualify to sit for the CPA, and they are inclined to see their education as complete. It will be interesting to see how the credentials for CFO roles, etc. change as our generation gets more and more senior. For now, I think many CFOs only have CPAs, but I think it will be much more important for them to have broader business exposure in the near future.
I do think that more important than convincing the admissions team of your qualification for an MBA program, is convincing them that the MBA program is necessary for you to end up where you want to go. So I would focus more on that side of the equation.
4) Recommendations? I had my closest manager and my department's executive director write mine. Both are people I have excellent working relationships with, and both have had significant exposure to my direct work product, as well as have witnessed my managerial skills in action. I did leverage their previously prepared feedback from our formal review system to help frame my request- i.e. they both received packets with drafts of my essays, highlights of our working relationships including quotes from favorable feedback they'd previously provided.
Regarding other posters who've taken similar paths, I know Nink is ex-Big 4 and ended up at Yale (has he graduated now?). Hope that helps!