If it's a G string... I'm guessing it's a trem style bridge... maybe a Strat style bridge... There are different ways to adjust intonation... I tune to the open string, then play a harmonic at the 12th fret and tune to that by adjusting the saddles.

It may just be your bridge moving back and forth if it really is a strat trem style bridge... They're notorious for going out of tune easily. Especially if you have it set up lightly with 3 springs and you use it a lot. It's never going to stay in tune very long. If you don't use your trem I suggest installing 5 springs and tightening them down... This will give you more tuning stability.