There's definitely some tricks that can help out with the clicking. A multi-band compressor is kind of a no-brainer. Set it up the right way and you have yourself a nice de-clicker, and you can dampen a lot of the clicking without making it sound all mushy overall.
The secret to a lot of this stuff, as you've already ventured a guess, is in the right-hand technique. Ever notice how chicks just all seem to love bassists? It's because of their highly-developed and agile right hand fingers. Okay, I just made that one up. But seriously, the biggest differences in tone you will hear comes not necessarily from "how" you pick as much as "where" you pick.
Example; if your hand is directly over one or both of the pick-ups while you play, then it will likely sound like a plickity-pluckety mess if you're not careful. Now if you move your right hand up or down, you'll find sort of a sweet spot that's more forgiving, and where your bass responds and sounds really good. Usually this is between the two pickups (assuming you have two) ... or perhaps just a bit lower down from where you normally play. If you're a forceful picker, then by all means, move down to where the strings have more resistance. The higher up (closer to the fret board) you get, there's too much slack, or "give" if you're a hard plucker.
You see, a lot of people just pick way too forcefully to begin with. And this isn't just with bass, either. A lot of people just play like they're angry
and they think it's pretty rockin.' Like in their minds, they're playing heavy metal in an 80,000 seat stadium or something and they're getting to an emotional part of the song that just RAWKS, so they have to really TEAR in to those strings like they mean it.
And it's kinda' funny, because I see the same problem with some kids when they play accoustic geetar. Like they really think they're rocking or something because they're just tearing in to the strings with their heavy pick ... and they think it's going to come accross as sounding more loud and powerful ... like they're Kip Winger or something.
Playing with controlled intensity is where it's at. If you want something to sound more forceful, then you need to learn how to crank up the intensity and play more
deliberately as opposed to more forcefully. Ya see, when you play more forcefully, you're actually achieving the opposite of your goal ... instead of sounding louder and fuller, you just sound thinner because the sound of the pick (or finger if you're playing bass) attacking the string over-rides and dominates the tone and resonance of the notes and/or the chords.
It's a very similar phenomenon going on when singers try to hit higher notes ... or when they want to project more and sound more powerful. Ya see, when you reach for those notes or intense vocal passages, the idea is to
relax and open up your vocal chords. Not tighten or strain them. My brain still can't grasp that concept, or I would have been a good singer by now.
I'm babbling now and getting off on a tangent, but it's a principle that's important when playing anything ... with the exception of drums.
You should pretty much beat the hell out of those if you want more tone. That's all.