Do you have council collected wheelie bins? If so make full use of them.
Find out which side gets emptied first (your side, or across the road) and fill your bin and place it on that side. Wait for it to get emptied then refill it with bags you have waiting and put it back out (on the other side of the road) to be emptied a second time.
If you have friendly neighbours, you might want to talk to them and ask if they are willing to let you put an extra bag in their bin (if they have extra room) each week. But if you do so, make sure you only put clean bags in their bins. You don't want to make their bins dirty.