Any traces of bleach that are left in your tank wouldn't harm very much. Once the tank is filled the concentration of bleach becomes very low. You could add some charcoal to your filter to be sure.
You should always wash new plants with tap water before adding it to the tank. Plants might have pesticides on them or can bring animals in your tank. This is all I'd do to clean them. On the other hand, I've never seen any snails or other creatures on the plants I bought.
others use bleach (mostly H2O2) or salt water to clean their new plants. But I wouldn't recommend bleach myself.