I have gone with backpacks (up to 8x10), but for a 11x14, perhaps a wheeled hardcase piece of luggage? Of course, wheeling a big piece of luggage around town might get some strange looks. A line from a short story that sticks in my head -- "Daddy? Is that man homeless?" "No, Honey, that is a man with problems."
Richard Ritter in his instruction video for his 7x17 camera suggests a large suitcase (his was soft-sided). I have one (7x17) on loan and am using the cardboard box my iMac came in -- it even has a very substantial handle. Camera fits in perfectly along with a holder -- I'll have to have the lens and etc's in a daypack. I just won't be using the box once the rains start!
And there is always the baby buggy route (larger wheeled jogger style).