Size 13 is probably too big for a single strand of Cascade 220. The bigger the needle, the looser the fabric, which means it has to felt even MORE to get a nice, firm finish with invisible (or nearly invisible) stitches. So...if you used size 13's (which are quite a lot bigger than the 10 1/2's the pattern calls for), your bag might get pretty small once it's fully felted.
Double-stranding with the 13's would be fine. Single-stranded on 11's is probably okay, too, but 11's are actually quite a bit bigger than 10 1/2's, too. (1.5mm bigger, to be exact. The US needle sizes make no sense. Heh.)
Good luck, booga bags are fun.