I don't have experience with "bunkers," but I have left my live well running overnight on several occasions, using shore power, with anchovies.
I do this as 1/2 a scoop of live anchovies (which is actually two rather large scoops) in San Francisco runs $30.00, and you get a ton of chovies. We can't possibly use them all in a day fishing for halibut. Also, the live bait operation closes at 9:00 a.m., and sometimes I can't get there in time. So, I choose to run the livewell overnight, and fish two days running.
However, one morning I returned to the boat with two inches of water on my deck, with anchovies swimming freely. The livewell overflow tube got clogged with dead chovies, and the tank overflowed, thus leading to dead anchovies plugging the deck drains.
After that, my dealer sold me a device designed by another Grady owner (made of pvc, with a solid top with vertical slits on the body of the tube), that slips over the original tube, which prevents dead anchovies from clogging the top of the overflow tube.
I am not overly concerned with burning out the pump. I assume it was designed for extended use, and running overnight is no different that running all day.
Tim