If you’re willing to spend $32 on the problem, here’s a more elegant solution.
https://www.amazon.com/Camco-Winteri.../dp/B0000AXQU2
You will fill this small tank up with a dilution of bleach, then hook it to your tank fill valve, then use city water pressure to push the bleach into the freshwater tank.
Obviously this can be done a dozen ways just with stuff from the hardware store as well. There’s no “right” answer, just lots of opportunities for solutions. I’d probably try making a pvc canister with valves on each end if I was going to do this very often before buying this, or as you say, just get an empty hose and pour bleach down it, then hook to the tank fill...