Bleach is a no-no, rinsed or not. If you can smell it, you breath it. Bleach sends people to the hospitals. Peroxide is better, but still bleaches, and does not tick all the right boxes with regard to the durability of the mix, cost etc.
The best way is to use a quaternary ammonium. There are a few on the market, but the Didecyl is the best one for such application : 2.5% w/w will kill the biofilm under one hour. Other quaternary ammoniums are ok, but they may have a sensitivity to hard water, some are more potent than others on algae etc. The Didecyl deactivates in contact with biomass. It is all in the dosage. However, any spill / run off will not leave a durable footprint.
I run roofclean dot co dot uk and renderclean dot biz in the uk: You can download the safety data sheet and take note of the CAS No before the trip to the shops. It should be on the label.
Mind this ladder - Francois