A Harris poll that appeared in Bicycling magazine found that one of the main reasons more people don't ride their bike to work is a lack of shower facilities on site. As you will see, this concern is often misguided.
First, a shower is not always necessary. Only some 20% of bicycle commuters actually shower at work. In the early morning hours when commuting typically occurs, the air is cool, and sweat evaporates. The constant breeze can keep you drier than if you stood around waiting for the bus. Taking a few minutes when you arrive to cool down in the building's controlled climate and a bit of deodorant also help. There is the further option to take it easy on the way in as not to work up a sweat, then to ride to get a workout on the way back, where you can shower and change when you get home.
Choose Smart Clothing
Showers can be further avoided if you ride in a lycra outfit, or other sports clothes designed to wick away moisture and keep you cool and dry. (Cotton is, in my humble opinion, an evil fabric that soaks up water and makes hot days or hard rides unbearable. A bare chest is much preferable.) At the very least, wear a lycra jersey and change at work -- this will eliminate nearly all of the overheating and sweating problems. Clothes made of advanced fabrics are even more advantageous if it's cold in the mornings but the ride home is hot and hard, where thermal cycling clothes are the only thing which can keep you comfortable through both hot and cold.
In any case, a quick sponge bath and towel down in the washroom is probably all you'll need to feel clean and refreshed. Track down a wheelchair-friendly washroom with one of those big, low basins, which are usually single-occupancy as well.
If you truly need a shower after cycling to work, you may be in luck. Many employers already provide showers and changing facilities for employees whose work is dirty and strenuous, even in office buildings. Some employers have incorporated showers and changing rooms within an employee fitness center. Otherwise, a nearby public fitness center may allow you to use their facilities for a minimal charge. From there, you can walk or ride slowly to work.
If the absence of a shower is preventing you from commuting to work by bicycle, how about asking your employer or building owner to install one for you? They might not have been aware of a cyclist's need for a shower, and they just might take to the idea. Once you tell them that shower facilities help retain health-and environment-conscious employees and promote employee wellness and improve the productivity and mood of their workers with a relatively low investment, your wish may be granted right away.