Depending on your level of fitness, 11 miles isn't really a lot, and will probably reinvigorate you after your long shift. However if it's pissing down with rain or howling a gale or all up hill on your way home, it's probably something you can do without.
Maybe best to stick with the scooter.
I have been "feeling my age" lately, after a couple of operations this year and some health problems which I don't seem to be able to shake off, and I've thought of getting a car, but I don't think I could face the traffic. I'm resisting the urge to "go lighter" with a 250 or something, but I think it's inevitable in the long term.