On an amplified instrument such as the electric bass, a lot of technique is about preventing notes from ringing. This is very different from acoustic instruments where a lot of focus is on getting notes to project.
Typically, bassists play one note at a time. Part of the rhythmic impact of a bassline comes from playing notes cleanly and individually. If you let notes bleed over one another or have unintentional notes ringing, it takes away from the attack of the next note. That weakens your overall bass sound. It will sound sloppy, and it can kill the rhythmic feel of the line.
Open String Troubles
Open strings on the bass are one of the hardest aspects to control. They often ring when they're not supposed to. Sadly, a lot of bassists avoid the very useful open strings because they're hard to handle. Don't! Learn to use them with confidence.
You just need to do a little focused practice to keep the open strings from getting in the way of a nice, clear bassline. It's worth the effort.
The Two-Handed Silent Treatment
Both hands work together to mute the bass strings. The strings below the note you are playing (below in pitch) get muted by the plucking hand; the strings above get muted by the fretting hand.
For example, if you're playing any note using any finger on the A-string, the lower E-string is muted with the thumb of the plucking hand, and the higher D- and G-strings are muted with the first finger of the fretting hand gently resting across them (not pressing down!).
This silences three strings while one string sounds the intentional note. All strings are addressed all of the time. If you have more strings, you have to mute them all.
Open String Muting Exercises
In this lesson I am giving you some exercises emphasizing muting of the open strings—especially with the fretting hand.
Plan to be frustrated. I've terrorized students with these open-string muting exercises for years.
They sound very simple, but to play them cleanly takes a lot of muting skill and precision.