My favorite method --
a semi-hollow bass, like a Gibson EB-2 or a Guild Starfire.
If I ever get my hands on a Starfire II, I'll pull the frets and fill them in.
Flat wound strings, either nylon tape or flat steel.
A little foam under the bridge, yeah yeah.
Here's the difference: play over the high end of the neck, not over the pickup or near the bridge.
This roughly corresponds to where a standup player would be fingering the acoustic bass.
It gives the note time to "bloom" and fill in the fundamental tone, without popping the high harmonics too much.