That's the exact reason for switching to bleach is to prevent cya build-up which causes chlorine lock (reduces effectiveness). CYA will come down over time necessitating a switch back to dichlor. You need more than a tsp of bleach though. I thought I read that it's a quarter of a cup but I forget the exact amount. When I did this program I never actually measured it out. I would just pur a "glug" in after each use and it worked out. Occasionally I would pour a larger amount of bleach in.
I have a good size 6 person tub and have found about a tablespoon of dichlor when the two of us use the tub after showering is about right and when the stabilizer reaches 50ppm I switch to bleach. About 1/3 cup of household bleach = 1 tablespoon of dichlor. Be careful with the bleach you buy. Pool bleach is good as is non scented and not the thickened easy pour bleach. Both of them will cause foaming. Good old Clorox works good but you pay a little more for the name.
When the stabilizer drops to 30ppm switch back to dichlor.
The number drops slowly and if you add water it will drop.
We live where it gets very cold mid winter and if I’m ready for a water change and to lazy to drain and clean the tub I will just drain it half way and refill and it gets me a couple months to warmer weather. When I do that I have to start back in with the dichlor for a while.