Using a fairly deep baking dish (9x9 inch pyrex pan), place a bed of chopped lettuce on the bottom, then lay down a layer of celery, then onion, then green peppers, then peas, then eggs. The order is really not that important, and they will nor really constitute a solid layer. Then and another layer of lettuce and repeat the procedure.
Mix mayonaise and sugar together and spread on top. Sprinkle bacon and cheddar cheese on top of the whole thing.
Cover tightly and leave overnight in refrigerator, allowing mayonaise to permeate the whole thing.