You want the largest aperture - which equals the smallest f number - available. So, with your lens at 55mm, that would I
believe be f/5.6. For out of focus backgrounds, this is actually a moderate f stop; you would have more success with a
faster (larger aperture) lens that goes to f2.8, f/1.8, etc. F/2.8 zooms are available, but if you want even less depth of
field, you pretty much have to go with a fixed focal length lens such as a 35mm or 50mm f/1.8.
Before buying a new lens though, make sure you are shooting your current lens wide open - at its largest f stop. Go into aperture priority mode and use the smallest number available. See how that works and go from there. Subject distance, background distance, and focal length all play a role too.