There's a small amount of excess lye in bleach that could contribute to a small rise in TA, but it may also be evaporation and refill with tap water since that adds everything that is in the tap water to the spa (e.g. TA and CH).
Adding acid to have the pH lower should lower the TA as well. If you want to lower the TA faster, then lower the pH to around 7.0 and aerate the water and add more acid to keep the pH down. Every addition of acid will lower the TA.