Giving up plastic bags is right up there with kicking any addictive habit. Alcohol, smoking, chocolate and coffee. Worse, plastic bags are free or inexpensive, convenient and don't harm you personally so there is no death based motivation giving you impetus. (Unless you are a turtle or any other animal that gets caught in one of course.)
After a few false starts, these interventions seem to have the highest success rates.
Remember - like any habit you are trying to kick or a new one you are trying to start, you might have to have a few runs at it before it finally sticks. Don't give up. Just start again like it is your first day.