I solved the hair problem by cutting it super short.. though now I have bangs that require a short stint with with the flat iron, because I am no longer working/commuting.
Basically, I did what Indigoiis does. Except, instead of Baby Wipes, I used bath cloths. You know, those things that are for people who can't take a bath. When I got to work (earlier than everyone else) I would put the cloth in the microwave as required, while I cooled down and gathered my stuff for the the bathroom. I didn't use these every commute, since they are expensive. Sometimes, just soap and a washcloth underarms, on my back, and face.
I can't put a rack on my road bike, so I brought my clothes in every Monday for my 2x a week commute. However, I always kept a pair of black capris, shoes, bra, and jacket at work, so if necessary, I could stuff a shirt in my pack (really just a Camelbak with the bladder taken out) and look fine.