I wouldn't worry about antibacterial, myself, thorough handwashing is more effective & less risky in terms of developing a resistant bacteria population. But if you're really concerned, lavender, cedarwood and rosemary essential oils are all antiseptic.
Ivory is basically lard soap. Lard soap has been used for hundreds of years to clean bodies, hair, floors, dishes & laundry. It's no doubt better for your skin than petrochemical detergents. I still use soap myself for handwashing. I'm sure Ivory has added stabilizers, bleaches, scents & junk like that, though; have you tried Googling "ivory ingredients"? "You might also have issues with buying from the corporation that makes Ivory.
Dr. Bronner's is a really good, economical natural soap from a small, ethical, environmentally responsible company. The liquid can be diluted half & half with water for use in a handpump, or 1:4 for use in one of those pump foamer things. Also comes in bar form. The price might look steep but a little goes a long way!
It's available lots of places online, besides health food stores Fred Meyer's (Kroger's) and Safeway carry it (although at inflated prices). I think the company site is www.drbronner.com
. They don't sell it, but they list sources who do.
Another natural brand, cheaper (but not necessarily more economical if ykwim), available at Albertson's & Kroger among other places & also online is Kirk's Coco Castile. This is a bar soap made with coconut oil.
You also might consider making simple cold-process soap yourself, which is easier than you probably expect. www.thesage.com
have lots of info.