Sarah De Belen, a 35-year-old mother of two from Hoboken, N.J., says she uses about 30 or 40 plastic bags at the grocery store every week. Late last year, she saw a woman at the supermarket with a popular canvas tote by London designer Anya Hindmarch and promptly purchased one online for about $45. But Ms. De Belen says she soon realized she’d need 12 of them to accommodate an average grocery run. “It can hold, like, a head of lettuce,” she says. Besides, she adds, it’s too nice to load up with diapers or dripping chicken breasts.