| You mean in a pick-up, or in a bass?
Pick-ups - there are loads.
Many rockabilly players swear by Underwood. Fabulous all round pickup, simple to use, simple to install.
Shadow do a good copy of it.
Then there are many similar ones ... K+K Bassmax / Revolution Solo the list goes on. Some you can buy on ebay dead cheap, varying quality. All piezo electric transducers that fit in the bridge slot. All good.
If you like the sound of your click loud, you might need a clicky pickup to blend with the main pick up. Some people DIY this, but you can buy dual pick-up systems. K+K Rockabilly+ is prime example. But then you have the whole issue of impedance matching and tone blending ... the K+K comes with blender preamp for this purpose. More knobs to tweak, batteries to change etc. Easy, but tiresome.
For jazz / classical there are pickups like David Gage Realist, Fishman Full Circle, FishmanBP100 ... fit in different ways, not popular for Rockabilly. There are also lots of very expensive pickups which you don't need for rockabilly.
For loud psychobilly, you might want to use steel strings and a magnetic pickup / clicky blend. Mag pickups fit to the end of your fingerboard.
But go browse doublebasschat.com
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It is not a 'cello my dear
1937 King Mortone, Lamberts Deluxe; 1938 Kay M-2, Guts/PsychoSlaps; 1968 B+H Excelsior, Guts/SilverSlaps
myspace.com/jump66blues; myspace.com/4stringsking | 
I would suggest digging through the rockabilly forum.
