I wear a bike jersey, bike gloves, headtube and sometimes cleated shoes along with regular pants. I don't wear padded pants on the recumbent, but I do on an upright bike.
At work, I strip down and cool off. Once sweatting has stopped or reduced, I change my top and baselayer for a clean one that was stored in my locker.
Then I hang up my tops and gloves etc. They either drape over my bike or the bike stand.
We're lucky that the room gets morning sun, and is air-conditioned. So damp stuff dries out in a few hours.
I wouldn't normally wash or rinse anything, and I don't generally have a shower either... riding the recumbent makes that slightly unnecessary.
However I do have to make sure my seatpad gets sunlight/drying time too - that tends to absorb sweat over the commute.
At home-time I'll re-wear the original clothes, which go in the wash at home. The day's clothes get stored on top of my locker for reuse. I'll get a couple days rotating through several sets of at-work clothes before they need to go home for a wash too.