You need eggs in the bait box so they can raise a new queen.
Early in the spring when temps are still dipping down is when I like to leave the nurse bees on the frame, to keep them warm. When the temps warm up in the summer no need for nurse bees.
I mostly always take a frame of eggs when I go to set the trap out up, this saves another trip out.
Again, in the early spring the temps may fall and bees quit flying before you are completely finished setting everything up (not the case for you though). That frame of eggs/open brood has been sitting for several hours now, the nurse bees have regulated the temp of them and kept them fed. Now you put them in the bait hive and since the temp has dropped to where no bees are coming out of the cone to cover the eggs/open brood, the nurse bees can take care of things till it warms up the next day.
That is my reasoning on nurse bees in the spring, some trap outs I have set up might not get the eggs/open brood until late evening because it took that long to get everything in place.
