In your case you could perhaps strap a plastic bag to your lower legs with perhaps velcro closures, to protect the legs from road grime.
My workplace has showers and lockers that a bicycle commuter can use. What I have done in the past is to put my work clothes in a plastic bag and deposited that in a saddlebag. After arriving at work I would be lathered with sweat and would make use of the showers. However, other employees would lock up the available lockers (which is against the rules there), and over time, I became afraid to go in the shower barefoot but did not want to carry flip flops in the saddlebag, either. The weight of all my things bothered me a lot. Not just the change of clothes but my shower stuff too.
Today, I don't really care how I look at the office. So when I restart my bicycle commute (after a break of a couple years) I may just wear my cycling clothes. There are many employees and there is a very wide range in clothing preferences, so I don't think I'll raise any eyebrows.
Bob