There are other factors which you cannot quantify, such as the joy of adrenalin, seeing cute animals on your commute, feeling more alive, sense of personal accomplishment of beating your own record from last week, social connections with other bike commuters on your route like that guy who rides the red Trek who you are always trying to be faster than, etc (fill in your own). When you consider these qualitative factors, which you'll only be able to do once you've tried it--actually, in my experience, after you've gotten through the initial difficult stages and are used to it--then you might think differently of it. Time on the bike is worth 1000% more than time in a car, so I don't hesitate to spend more of it.
I don't have a shower at my job but I get around it like this:
1) wear bike jersey, shorts and sneakers while riding
2) bring work clothes packed carefully in panniers
3) washcloth, ziplock, towel, staff restroom stall
4) put on work clothes in restroom
5) switch into dress-up shoes which live in cubical
6) Presto! white-collar professional.
Your workplace may vary but if you have a secure location at work to keep your shoes and some items, and panniers, you can probably come up with some variant that works for you. It really isn't as much hassle as you think.