I love getting that blurred background where a bike or a person running past is in focus and you literally see the motion in a still image. Mango Street made a video to show how to do it with some great tips I had never even thought of.
Keeping the subject at the same distance as it passes by sounds more difficult than it is. Cars, bikers, and people crossing the street are all you need, and the shutter won't be open for too long, so it's long enough to remain the constant distance you need. They recommend closing the aperture to f16 and setting your shutter speed to a 1/30th of a second. Once you do this you'll be able to gauge what needs to be changed to get that motion blur captured. Shooting at f16 will have more of the image in focus, but with the motion you're adding, this won't be an issue. You'll still 'remove' the subject from the background by adding the motion blur.
- If 1/30th of a second is over exposing, you can add an ND filter.
- You can shoot in darker times of the day. Car headlights can add some great effects.
- Going out to shoot these type of shots is going to give you many misses, but every once in a while you'll go though your shots and be pleased with what you got.