If you have an opportunity, you might request that your employee install a wall-mounted dispenser stocked with shower gel, shampoo, and conditioner. We have one and it's a great thing. I'm bald, so I'm not picky about what's in it, but if I were it might be a different story.

They also installed a standalone coat rack / closet rod thing (designed for hanging clothes) that we are supposed to use to hang dry our wet/sweaty clothes. I guess people complained about sweaty workout clothes (or in my case, wet from washing in the shower cycling shorts/bibs) drying out in view of people working. The rack works really well.

So I shave and brush my teeth at home before I leave, and then just shower and dress when I get to the office. Bibs, jersey, towel hang on the clothes rack during the day and are nice and dry when it's time for the ride home.