Think of it this way--at least you don't have to lug a camera bag full of lenses, lighting gear and a tripod and your bank account still has a couple thousand dollars in it.
Depth of field depends on several factors, not just aperture. The size of the sensor (which is where your main handicap lies), the distance from the subject, the distance between the subject and the background, the focal length you use, and the aperture all play a part.
If you want to increase out of focus blur, then:
1. Open up the aperture (use a smaller f-number)
2. Increase the focal length/zoom in.
3. Move closer to the subject (this is why macro shots always have background blur)
4. Move the subject farther from the background.
The only problem you're going to have is that 2. and 3. may conflict. Typically the more you zoom in, the bigger your minimum focus distance (the distance you can be from the subject and still focus) gets. You may also want to try switching to macro mode.
Also, if you're reading about photography in books meant for SLR users, the depth of field corresponding to specific f-numbers can be deceiving. A 1/2.5" sensor is one sixth the size of a frame of 35mm film. It's DoF is correspondingly six times as deep at a given f-number as it would be on a full-frame digital camera. f/2.8 on a p&s is like f/16 on a full-frame, or f/8-f/11 on a crop-body.