I'm not an expert, but I will offer my two cents. I have to assume that you have a good supply of quality salt water. I would use two or three 5 gallon buckets, or similar plastic containers, and put salt water in the first two, maybe half full. I would wash the sand and rocks, separately, starting with the first bucket for the "dirty" wash. Move them to the second bucket to wash again, for slightly cleaner wash. If needed do the same in a third bucket.
As the first bucket becomes really dirty, pour that water out, and this becomes the new third bucket. The original second bucket now becomes the first dirty wash, and so on. Basically you are using the water until it is too dirty to continue.
After cleanup by washing in salt water, put the sand and rocks back in the aquarium with fresh salt water. Then watch the protein skimmer and set it for vigorous skimming.
Having said all of that, I doubt that major damage was done to the rocks and sand by the food items in the tank, and I would not worry about "bad bacteria." In other words, I doubt that long recycling will be necessary. But the sooner you start to get the crud out, the better for the good critters on the rocks and sand.
Maybe someone else on the bulletin board has more expertise. Good luck.