Bass tends to be non-directional, so you may very well end up annoying more than just those below you. However, some of the problem can be caused by direct vibration of your floor, so putting it up on top of something will likely help with not bothering the neighbors below you. A thick rubber mat might work, though others may have better suggestions. Really, without having any idea of the construction of the building, or how loud you like to listen, I have no way of knowing how much you are likely to bother your neighbors. My advice, after isolating your subwoofer from the floor, is to talk with your neighbors right away, and tell them that you don't want to annoy them, and let them know that you will be happy to turn down the volume whenever they ask (assuming, of course, that you are willing to do that, which you should be). You may wish to give them your phone number, so that they don't have to get dressed to come up and complain. I assure you, that talking with your neighbors, unless they are extremely unreasonable people, will be the best thing you can possibly do.
Edited to add:
I sure wish all the neighbors I have had were as interested in not annoying me as you seem to be.
