i commute 5-11 miles to jobs and school, in the summer i wear my cycling shorts/jersey.

if im only going to be at, say, a class for an hour or two, ill simply change into a normal shirt and put a pair of normal shorts/pants over my bike shorts and throw the jersey into my bag

if its a day you get gross just give yourself a little extra time and bring a whole change of clothes and do the locker option (which i have done also)