I've never had a problem with condensation on my drain line. Mine is PVC pipe, is yours metal? You could try putting pipe insulation on it to keep the warm humid air away from the drain line.
As to the bleach, I wouldn't put more than a tablespoon in a nearly full pump reservoir. I just installed a new toilet the other day and the specifically warn against products like 2000 flushes saying it will void the warranty on the rubber parts. In the pipe itself, you could put more to kill off any algae growth.