I'm all over the map with trying to get "that sound" - to the point where I run my basses into an MXR M80 DI prior to amplification. I just don't play without it...yet. It just seems to add the fullness that I can't achieve with my low-budget amp setup. I was in GC yesterday, and I played three basses that I currently own through higher end rigs (without the MXR, of course), and they sound magnificent. Someday, I'll own a nice rig.
The mistake I made, and I doubt if I'm alone, was to assume that a sound I liked with the bass on its own would also sound good in a band. It didn't. At one time I had a pedal board the size of a small kitchen table with some wonderful, expensive toys in it, and I spent ages concocting killer tones which, when the band came in, disappeared in the mix, or sounded like a fart in tin can. In the end, I thought to hell with it and sold the lot, apart from a SansAmp BDDI I keep for an emergency that has yet to happen.
I also have what most people here would probably regard as a laughably low end rig - a Hartke HA3500, bought cheap, used, on eBay, an Ashdown Mag 2x10 and a Mag 1x15. Bass tone controls are all set to maximum treble. All I use to adjust to different environments is the high and low pass contour controls on the Hartke. People who aren't my friends tell me this sounds good.
Like Kenny I change tone by the way I play. Unlike Kenny I have no idea how I do it. Well, I do, sort of. I hear the tone I want in my head, and it happens. I always use a pick, too, so I can't explain how that works, but it does.