131 was the number thrown around in other comments. And I replied there as well, but go ahead and add it up - if the bag holds twice as much, and you use 2 bags a week, we're talking about less than a year before you are ahead of the game.
> one study from the Danish government found you'd have to use an organic cloth bag 20,000 times for it to be a better environmental choice than plastic
I think "better" is very subjective here. If we're talking the energy and water to make it, sure. But that probably pales into comparison compared to the produce you'll be putting in those bags anyway.
With all we know about plastic in the environment now, and how ineffective recycling as a strategy is, I think anything that will harmlessly biodegrade in a reasonable amount of time is a better choice than plastic.
(Which is where Denmark is coming from: http://www.seas.columbia.edu/earth/wtert/sofos/Denmark_Waste...)