I am well versed in hygiene and food safety for professional reasons, and there are a couple of considerations here.

First, it's been a while since the main "antibacterial" soap additive, triclosan, was banned for household use in the US. In the EU it has never been on the approved list. The reasons range from lack of evidence of its effectiveness to the need for limiting its use to medical environments to prevent the development of resistant bacteria, and to minimize wash into the environment which may affect other non-target microorganisms. So, what type of "anti-bacterial soap" are we talking about?

Second, again for household use, the single most important thing you can do if you currently wash your hands with "plain" soap and water is simply to wash them for a bit longer. Soap does not kill microorganisms, but it does "catch" them and carry them away when you rinse, as it does with all sorts of harmful organic and inorganic substances, which hand sanitizer or "antibacterial" products just don't. Plain soap is actually extremely effective at that. So unless you have some reason to want the bacteria in your hands specifically dead when you send them down the drain, there is no need for any "antibacterial" product.