I am lucky enough to have lockers/showers at my current job but at a former job I had nothing but a shared bathroom with other business on the floor.
* I was able to alter my schedule so that I was there early. I very rarely encountered anyone else in the bathroom and when/if I did the ladies were generally very cool about it.
* My commute is very hilly. I arrived sweaty. Some days I took a bus part-way to work to minimize sweat factor.
* I took sink bath after cooling off. Hobo shower?
* Hair is not a problem as it bounces back after adding a bit of water and fluffing.
* Keep extra bath products and makeup at work.
* Change clothes entirely if you sweat. I find that my wool is great at having no odor but sport bras not so much. Strip everything off and start base layers clean and dry.
Most people had no idea I rode unless they saw my bike in the office.