First question: How flat is it?

If it's fairly flat, then with an 11-mile round trip, 5.5 miles each way, practically any bike will work. I'm riding an industrial cruiser bike, and that would be no problem on it.

If it's hilly, then you need the gearing, and that complicates it. If you're riding 55 miles instead of 5.5, it might be a bit more critical what you rode and what you wear while doing it.

At 5.5 miles, you don't need specialist clothing just to ride- jeans and t-shirt will likely work fine. It would help to have some way to shower or change clothes when you get to work, though.