The OP wanted some general pointer to play tetrachords. Two of the pointers given will work:
1. to take notice of the next chord and use the notes of that chord passing through the tetrachord (like Slybass wrote, a very versatile approach)
2. to use the notes of the key scale of the piece (like I wrote, a functional harmony/diatonic approach).
Yet it all comes down to taste. The tetrachord needs two whole tones and one semitone to take three steps, so the real question is if the semitone comes first, in the middle, or last.
For example, if Am7 is ii in G (Phil's example; however, vi in C is also possible), the bass needing to descend to D7, Slybass will play A - G - F# - E since F# is 3rd of the D7 chord. I will figure to play the same, since A - G - F# - E follows the G major scale.
However, to attain a real downgoing tension, A - G - F - Eb is stronger. So a third pointer might be: for more tension, the semitone comes last. If this tension is desired in a certain case depends on taste. this correlates with Slybass' example.
Now that we're at it, we could also discuss how to go up a fourth in four steps. F.e. going from D to G in G major, we shall need to put in a chromatic note. Would you play D - E - F - F# or D -D# -E -F#? And why?
Good question and I make a strong point in my basslines to support the color of the chord first of all. So the important beats in a bar for harmonic purposes are the 1 and 3. By playing the minor third on the third beat we are implying more of a minor then a major chord and even if it is a very typical line especially in a Blues form I try to keep that for the the minor chord and really focus on putting the major third on the 3rd beat or by playing the second line in your example. I love the movement of 1-#1-2-3 because it is actually the second tetrachord of the major bebop scale of the destination chord.