Hi Wendy,
In a nutshell, it's all about ...
(a) The distance between your camera and subject -v- the distance between your subject and the background. The smaller the camera-to-subject distance and the larger the subject-to-background distance, the more out of focus the background will be.
(b) Aperture (wider is better, but as you know, it also reduces your DoF).
(c) Lens focal length (think of it as a "Bokeh Multiplier").
On a D3000 @ 200mm @ F8 @ 1.1m your DoF is 7mm (so what is well behind is well and truely nuked)
At 40mm @ F8 @ 1.3m your DoF is 206mm. The background is still OOF, but because you're zoomed out a lot more, more detail is captured, which tends to negate the effect.
So in summary, use a long lens - get a smaller gap between you and the subject and a bigger gap between the subject and the background - and open up the aperture as much as you dare (but watch the DoF).
Hope this helps