I would consider riding in in normal clothes and changing into your cycling-specific stuff for the ride home.

If your bibs are sitting in a closed locker an hour and 20 minutes they may not get dry (if they're at all sweaty to begin with). If you're showering immediately beforehand it seems unlikely that your cycling gear is going to grow stuff in the time it sits, but changing will still take time before class. Over that distance the time spent changing is going to wipe out any time saved wearing cycling-specific clothing. If you're not working up much of a sweat on the way in that's how I'd do it.

I think changing into the stretchypants for the ride home is smart though. If you're already geared up to ride you'll be less likely to putter around at home and you can just drop your stuff off and go on your ride.