Just need to have enough bags to support a slow “when you get to it” rotation. Bags stay in trunk (you might need to double the number of bags you have to support a second vehicle), then grab a bag of bags when going shopping, fill bags at store, empty and full ones go in trunk when leaving store, full bags go inside to wherever is most convenient, then when they are empty, place them near the door. Then, on some trip to the car, remember to grab the bags by the door and stick them into the trunk and you’ve completed one cycle for those bags.

If they get dirty, put them near the laundry instead of the door and either mix them in with another load of laundry or do them separately if you’re getting that many bags dirty often enough to justify a load of bags. If they aren’t specifically dirty, they should be fine. They aren’t like clothes where you’re slowly sweating and getting skin oils into them so need to wash them on the regular. Just turn them inside out to make sure the bits of onion skin all get washed out.