#1
I'm just getting started on playing lead and picked a Ventures song (Walk Don't Run) as the first song to learn. I figured that it's recognizable and not too hard for a beginner. While things are coming along OK, I did run into one issue that I need some help with. Here's the relevant part of the tab:

E :----------------|----------------|
B :----------------|------1--0------|
G :-2--------------|-0-2--------2---|
D :----------0-2-3-|----------------|
A :---0-2-3--------|---------------0|
E :----------------|----------------|

In the second measure, you pick the B string on fret 1, pick the same string open and then jump to fret 2 on G. What is the right way to mute the open B string so it doesn't ring over the next note? The same thing comes up a bunch of times, but this is a good example.
#2
Mute it with your fretting hand; the finger you use to play the next note on the G string should also lightly rest on the B as you fret to keep it quiet.

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