From everything I've seen, minor league pitching and hitting (and maybe bench) coaches look for Major League jobs when their Pitch/Hit rating gets to 75 and up. If you look at career Bullpen coaches their rating maxed out at no more than 74.
Now if you want to get ahead of that curve you can offer your AAA coach the Bullpen job when he's not asking for the ML pitching job. Just be aware that when he hits 75 he's going to want the switch.