I do similar, but add one (to me, vital!) step. I always wash my hair again after getting to work. For some reason the majority of my sweat on the 7 mile trip collects in my hair, and if I don't wash it regardless of the fact that I washed it minutes before getting on the bike, it feels nasty halfway into the day. So adding in a sink "shower" for my hair makes the world of difference.

Granted we have showers here, it's just getting someone to clean them out so I can actually use them (when the training rooms were built up instead of the gym, everyone decided to use the showers for a storage area...)