The free, single-use plastic bags were perfect for our 20 litre garbage bin. Now I have to buy 30 litre garbage bags (the minimum size available) so, on that alone, the change means we are using 50% more plastic.
We still accumulate reusable bags, though at a lower rate. So much so that I have to start using them as garbage bags, to thin the herd. The takeaway from this is that the 10 cent charge is way too low.
The reusable bags were great for other things also: taking things for recycling, wet clothes from swimming, going to beach, etc. The reusable bags are bulky so other types of plastic bag are pressed into use and hoarded.
So we got at least two uses out of the previous bags: one trip home with groceries and another trip taking out garbage/recycling.
What did make a substantial difference to our household's consumption of plastic bags was that some supermarkets (here in Portugal) offered, free of charge, heavy-duty, hold-all style bags for a short period of time. These are long lived and infinitely preferable to the single-use sort.