This should be the first and easiest step towards a plastic-free life. We're very lucky in Aotearoa NZ where single-use plastic bags have been banned for over a year now (although some cheeky takeaway places will still get plastic sacks and make a knot as a handle).
But not so lucky with the replacement for that. Unfortunately, the majority of supermarkets are still offering the non-woven polypropylene "green" bags (the black, red or yellow ones, depending on the supermarket).
These bags are not as innocent as you might think. Made from a by-product of oil refining, this is a fossil fuel-based plastic and hence made from a non-renewable resource. It supposed to last 2 years/100 uses, but I've seen some breaking after the second use. If you have them already, don't panic. Instead, please keep reusing it as much as you can and at the end of its life, take it to a soft plastic recycling station.
The other available options are paper bags. These can be recycled or composted but they don't last very long so we can't call it reusable. Again, if you already have it, make the most out of it and at the very end, you can use it as a rubbish bin liner.
The next time you buy shopping bags, choose the ones that are made from natural fibres such as ethically-made organic cotton, jute or hemp. Cotton bags are made to last years and their time has come, it can be home composted. Just be mindful that fabrics will take 6 months or more to break down.
To avoid buying any unnecessary bags, the best solution is remembering to bring yours to the store.
TIPS TO REMEMBER YOUR REUSABLE BAGS:
Put a reminder on shopping list - the first item on your list can be "bring reusable bags"
Tie them to your purse or doorknob
Place them on the floor in front of the front door
Set a calendar reminder
Keep bags in your car our in your handbag/backpack
IF YOU FORGOT YOUR BAGS:
ask for a repurposed box,
carry the items in the trolley/basket to your car
carry the items in your handbag/backpack
ask for second-hand bags, many supermarkets have a box with used bags that you can "borrow" - if they don't you could suggest it
Happy Grocery Shopping!