I know stuff on muting has been posted a thousand times but there seems to be a thousand techniques to this.  I need a bit of help on what I am trying to achieve here. 
 
I been playing bass for around a year and I didn’t realize the importance of good a muting technique until I started recording myself!  I am self taught so have taken a few easy routes that involve not muting much with my plucking hand, apart from resting on the lower string with walking fingers. 
 
Anyway, the following common technique is what I am currently working on with my right plucking hand (I use a 4 string bass): - 
 
Thumb resting on pickup when playing E string 
Thumb resting on E string when playing A string 
Thumb resting on A string when playing D string 
Thumb resting on D string when playing G string 
 
When going from G string back to low E I use my ring finger to rest on the string I just played, I’m finding that a bit clumsy at the moment but it’s the only way I can seem to mute from higher tone to lower tone strings. 
 
Overall this seems to be the most natural way for me but I need to know if I’m going the right way with the thumb and ring finger muting before I start investing a shed load of time in this, is there a more efficient way?  For some reason I’m not into floating thumb, I just don’t like the feel of it but resting can take more time to manoeuvre I’m starting to realise, I’m hoping practice will address that issue. 
 
I’m looking to get a really clear sound with my playing and am willing to invest a lot of time on it.  I’d really appreciate any feedback on this.  
 
Ritch