You're on the right track with the soapy water, but not all soaps are created equal in the bug killing department. Though all of them are formed by the interaction of fat with an alkaline substance, if that makes any sense, the number and nature of fatty acids they contain varies quite a bit. I know this might not matter when your doing the dishes, but it can mean a lot when we are trying to cope with an aphid invasion on your indoor plants!!
So before you give up on soap, try a product specially formulated for houseplant care. At Botanica Gardens we have several different soap mixtures. Not only are they more likely to do the job for which it is intended, they also are less likely to burn the leave of sensitive plants.