I've taken a bike daily for years, for one commute the alternative was walking, which took around twice longer. So between getting wet on a bike and spending a longer time walking and getting wet, it didn't change much. And once at school, clothing dried quickly enough that it wasn't much of a bother. Later, when I had switched my commute to bike + train, the other option was to take a bus, but I never did it, because I just couldn't stand to wait for the bus and risk missing my train and getting late to school/work.