Bret - distance to target and distance from background play a major role in bokeh also. Generally, the (physically) closer to your subject you are, the more background separation you can get.
But the aperture of course is the other major factor. Don't forget when you're shooting in bright direct sunlight, it can be difficult to get any background blur because the aperture is closed right up (high f stop). Here, I want background in focus for effect, which is just as well, as it's a bloody bright day:
Whereas here we want soft and fluffy, a good framed shot, but using the focus to drive attention to the hand:
Regarding lenses, if you get a 50mm (equiv) 1.8 prime, and FORCE yourself to use it, you'll find you become much better at framing shots in general, you'll need to zoom with your feet, and you'll quickly learn to work the aperture to your advantage