The bloom is the protective coating on the outside of the shell. If you wash off your eggs, they need to be refrigerated afterward. They will keep for quite a while. Store bought chicken eggs are washed and they last for weeks. I rotate my eggs in cartons in the fridge on a first in-first out basis. I always put the narrow end down and the fat (air sac) end up to help the egg retain its natural structure inside.
If I think my eggs may have been in the carton for too long, I submerge them in a cup or bowl of water. If they float, I discard them. If they remain on the bottom, but the large end rises so they are sitting on end, they are getting close to being discarded. If I have a bunch that aren’t in cartons, I do the float test on all of them, discard any floaters, hard boil any that stand on end, and put the rest of them in cartons according to which ones lie the most horizontally on the bottom of the water container, using the tipped eggs first. After the bloom is gone, the eggshell becomes more porous and air enters the egg little by little. Thus, the float test as an easy way to determine relative freshness.