No reasonable amount of bleach water will harm the tank but there are some things to keep in mind as well.
The bleach is normally sold shipped and stored at a much higher concentration than we use in sanitation so not likely a mix, far reduced from the normal straight bleach content of 6%, is going to harm any plastics we have!
Chlorine is an oxidier which means it loves to combine with organics and it is also something that gasses off readily when exposed to air. It combines/reacts well with things we want to kill or sanitize. But the reason we smell it around a pool, spa or when we drink treated water is that it is somewhat hard to keep it in the water!
We have to keep treating pools because the chlorine keeps blowing away!
That means the even in a tank which is not moving much, the chlorine will gradually gas off and be gone!
That is good and bad, depending on the situation. If you want to keep the bleach water in the tank for a week or two, it will continue to protect the water and tank from bacteria growth getting very high. good for keep ing water from one trip to the next?
But if we want to store the RV for three months, the treatment will likely not be good by the next summer, so we would need to retreat to be sure we were safe!
But from years in community well water treatement as well as breeding tropical fish, I knw there is a vast number of people who are scared to death of chlorine. They think of WW1 chemical chlorine attacks and make the jump to that being what we buy in a bottle for laundry!
Most of the older group will have grown up with their mother using bleach to clean their skivvies but now some are certain it is a deadly poison!
We live in an age where science and bad information are often used to promote nonsense, so do your own checking to avoid the noise!