Maintaining a hygienic, germ-free bathroom requires the right cleaning products. When it comes to toilet brushes, there is some debate over whether or not to place disinfectant in their holders.
People who support doing this say bacteria and germs can accumulate in brush holders, before being transferred back to the toilet the next time the brush is used. Soaking the brush in bleach will largely prevent this.
On the other hand, prolonged exposure to strong cleaners can degrade the plastic and other materials of toilet brushes. This might significantly shorten the lifespan of your brush.
Ultimately, whether or not to soak your brush in bleach is your own decision. In any case, you should clean your toilet brush if you want it to perform properly.