Career Change and MBA Timing

For those of you that made a career change and then went on to an MBA, how did you time the move? A little background on my situation:

Currently a 1st year associate at a LMM PE fund. Started in LMM PE directly as an analyst and have been with the firm a little over 3 years total, with an A2A promotion 2.5 years in. NYC based. Have decided that PE isn't for me and am looking to make a move to something more operational. 

I'd also like to get an MBA for a variety of reasons. The issue I see is that if I make a job change within the next 6 months, I would be applying to b-school <1 year after starting the new gig and would be requesting recommendation letters after a pretty short time at the new company. I could request from the PE firm but worry that leaving unexpectedly would burn some bridges. 

Alternatively, I could stay at the PE firm another year to get letters but at that point I likely would just stay through year 5 before b-school. This isn't ideal because I don't particularly want to stay for another 2 years and because I'd like to try something else before b-school.

Struggling a bit with how to time a potential career move around the MBA. Would love to hear from others who made a similar transition before the MBA and how you timed around the application.