Bleach turns whites yellow over time... especially if left unused for over a few months.

Maybe the issue is also your washing machine? If you make the first load of the day your whites then progressively go to the darks then you might not have as much of a greyness issue. Some machines store coloured water in the base which then goes on to taint the next load. Once I went from darks to whites and even though the whites were put into a seemingly empty machine they came out a pinky colour because the previous load had some new dark red clothes from which the dye had come out.

Do you have town water?