Do it! I loved the bike commute yesterday, and today I biked to the farmer's market, Aldi, and the library. It's addictive once you get started.
I work at the county health department. There are no bike-friendly amenities. I locked my bike to a basement emergency exit railing yesterday, and I brought a wrapdress that I put on over my shorts and undershirt all day. My dress, heels, and lunch seem to fit well in my backpack, but I plan to install a basket soon.