Welcome to Talk Bass Necos.

DC Hardcore... just sounds like home. Don't worry, you don't need to blow up your amp, that tone is pretty easy to get: play near the bridge with a pick into an overdriven SVT Head, out to an 8x10.
Otherwise, just pick up an overdrive, preferably something with an onboard EQ, and maybe tubes. I think the EHX English Muff'n may be perfect for getting that sound, but be sure to try out a whole bunch of ODs and distortions to make sure you really like what you're getting.
There really isn't a way to get that bright a tone without a pick, but digging in really hard fingerstyle might get you close.