"single coil hum"
If you can tolerate any Jazz bass, with blend set one way or the other, any single coil 51 will be more or less the same.
You can mitigate this with a good grounding system, and copper foil or shielding paint (see my 'upgrading a 51 Precision' thread) but, unless you get a split coil, you'll have to tolerate a bit of that. It's never bothered me, mostly. Crank the volume shut between songs. Any good studio will "have good electricity," and shouldn't present a problem there...
In most cases, you can arrange yourself in relationship to the amp such that it won't be a problem. Strat/J-bass players have been doing this for decades. However, if you're in a crummy bar, with crummy electricity, and neon beer lights on the same circuit as your amp, they can get icky, like any single coil.
Nordstrand, Lollar, Fralin and SD will all wind you a "split single coil."