You should find a book or article about progressive companies that encourage exercise, bike commuting "on company time." Photocopy some of the stats and leave it on that woman's desk!
Seriously, can you talk to your boss about it? Maybe s/he can put a stop to the nasty talk. Yea, those women are really just jealous. Don't let them stop you. My husband commutes a couple of times a week. Sometimes, when it's not convenient to do this, he brings his bike and rides at lunch time. When he first started at this company, he had just finished a lunch ride and was showering in the fitness center. He saw his boss in the locker room and got really nervous. His boss said, "Don't worry, I just got back from a run!" If you get your work done, who cares if you ride your bike?
I don't commute much since I moved to a new house, but people at school have been very supportive when I have ridden in. If someone is there early enough to see me transform from a cyclist into my professional self (without a shower) they are usually amazed.