Here's a link to the story:
Reusable Grocery Bags Contaminated with E. coli, other bacteria
So, what's the answer? According to the above article, a "thorough washing kills nearly all bacteria that accumulate in reusable bags."
I just washed a couple of my bags and hung them to dry. They did just fine, washed in the machine with a load of similar color items. The bags I make are cotton, with cotton lining, just fine for a trip through the washer (and the dryer, if you like).
I just finished this one, with a yummy cupcake fabric. It will be available in my etsy shop soon. And it's washable!