The vinegar is great for calcium ("lime") and other deposits. For tougher deposits a slightly stronger acid will also work--use diluted muriatic acid, sold cheaply for cleaning concrete. The bleach, on the other hand, will sterilize. (Don't mix the two.)
Two or three cups of bleach diluted in 125 gallons though won't make it, though. To sterilize human "wet messes" we use a 1:10 solution. I'd suggest using at least a couple of gallons to soak a 125. Work in a well-ventilated area--this concentration of chlorine won't outgas enough to really be a threat, but why chance it?
That said, I can't imagine any reptile-borne bugs being a threat to saltwater animals. I would clean for appearance and then wipe down with a new sponge and the 1:10 bleach solution.
For all but the vinegar, wear old clothes and do it away from any fabrics and desirable life forms (i.e., the concrete patio is great as long as you don't dump the bleach water or muriatic acid out onto your grass. Rinse/dilute fully.
Finally, let the tank completely air dry after bleaching. Chlorine evaporates very quickly anyway, but if you let the surface dry, you can be sure that no chlorine residue will remain.