These will help you arrive fresher, and they will still be fresh for the return trip home. Avoid cotton tops in any event, because these soak up moisture on your morning ride, and can build quite an odor stuffed into a pannier or gear bag waiting for the trip home. Shorter rides can be done more slowly and in simple street clothes. You've probably seen pictures of businessmen in London commuting in suites and bowlers. Casual shoes and loose fitting trowsers are all you would need for a two or three mile ride.
Some places of employment have shower facilities.
These are nice to have, but certainly not essential. You will find you simply don't need a shower, unless you live in a very warm and humid region. A much bigger problem than looking presentable, is finding a safe place to lock up your bike. Copyright 1999 Bicycling Life Website.