When I'm playing a riff, especialy if it is over multiple strings and with open strings, alot of times I'll hit a string but it will continue to vibrate after I want it to. Don't really have this problem on normal guitars but the mass of the bass strings keep them moving after I pull up after fretting them. Is this a problem with the bass, or hitting the strings too hard, or will I get used to it, or what?
Improve your muting technique. All you need to do.
practice muting the strings
Can you mute with a single finger just like normal guitar? I don't have this problem down further on the neck but at the end of it for the first few frets it's rather sloppy.
You can mute any way you find convenient, so long as you aren't pressing down on a harmonic node, so instead making a harmonic.