I have a longer commute (14 miles currently, used to be 19). I use some of the suggestions above, sometimes riding one way each day, sometimes alternating days with the motorcycle. I leave a pair of shoes in my office, and use panniers to bring clothing to and from work. I'm fortunate to have a shower at work.
You've had a bunch of good suggestions already, my advice is also to get a skinny tire (road) bike of some sort. You'll be much happier riding those distances. For commuting I like old road bikes from the 70s-80s. You can find them cheaply and the older steel frames often are easier to convert to a good commuter with racks, fenders, slightly fatter tires, that sort of thing. I'd add that for lights for a daily commute, spend a bit more for some rechargeable lights. You'll save lots in the long run.
Oh -- don't get too fancy for a commuter, either. As an ardent cyclist and bike nerd, I built a beautiful long distance touring/commuting bike a couple of years ago. Stainless fenders, rack, disc brakes, generator hub and lights, leather seat.. it was cool. I rode it 300+ miles solo down through Florida on one trip, and commuted on it regularly.
I took it to the downtown library a couple of months ago, locked it, walked inside for 20 minutes, and returned to find it missing. My new commuter is a lot lower buck but gets me there just fine, and nobody's stolen it yet. :-)