New bass player question

The meaning is that is a G chord (G, B, D, over B) where B is the 3rd of the chord and this is the effect that the composer want. In classical music we called this as a G chord in first inversion very common use in Jazz.

 

So you play the B

 

Yup, you would want to play the B as the first note for that measure, thats what the composer is asking for. It's helpful to know that the chord is a G chord and not a B chord because that tells you what other notes are diatonically available (G, B, D). If the chord were a B chord, the chord would be structured using the notes B, D#, F#. So given that this is a G/B chord, it tells you that you should use notes in the G chord but begin with B, if you chose to add more notes, other than B, to your bass line. Hope this helps!