When looking at a chord chart like the following,
D G/D D
Amazing Grace, how sweet the sound
Looking specifically at the G/D, is it true that typically the bass guitar plays the "G" and the acoustic would play the "D".
G/D means "G chord over a D in the bass" (the opposite of what's suggested in the question).
The confusion may arise from the fact that in piano playing the left hand plays low notes (generally) and the right hand plays higher notes, so when you saw G/D you thought G with the left hand and D with the right.
Instead, when you see the slash say 'over' - so see G/D, say G over D which is G chord over D bass note.