Currently I am very lucky to have a workplace shower, locker and towel service. I store my soap/makeup and other necessities in my locker.

I had a position at another place of employment that had no lockers, towels or locker room whatsoever. My ride is about 10 miles one way with lots of hills and there's no chance of not sweating. First I made sure that I could work an earlier schedule than most others. What I used to do is store makeup/other things in my desk at work. Then I would change in the shared (by the entire floor, not only the business I worked for) bathroom taking a sink bath as much as I dared (only was interrupted maybe once or twice - turns out people didn't like arriving to work before 8:00 am). This pretty much was it. I had, and have, a haircut that doesn't require much maintenance either. I buy clothes that either don't wrinkle or fold very carefully. I always pack my lunch in an extra plastic bag (leaks from the best food containers will happen). I have extra articles of clothing at my desk because you will forget everything eventually from bra to undies to shoes to pants. Pack your bags the night before.