I can easily pack a change of "work clothes" (used to include dress shoes), toiletries, camp towel and lunch in a small backpack or largish messenger bag. Having a shower available is strongly recommended, however. Built-in in hydration for the backpack isn't a bad idea either.
I've gotten lazy and haven't biked in in awhile, but I used to do it every day by heading into work about 30-45 minutes earlier than I would drive, swapping my shower immediately after I got up for showering at work, and compensating for a slightly longer commute. If you compare the amount of time you'd spend driving to a gym, working out, then driving somewhere else, it's a no-brainer, bike commuting kills two birds with one stone and saves you gas money. Or you can try what I did for a while and get up even earlier to bike to the gym, workout, shower, then bike to work, using the cycling as warmup and cool down for the gym workout.
I've gotten lazy and haven't biked in in awhile, but I used to do it every day by heading into work about 30-45 minutes earlier than I would drive, swapping my shower immediately after I got up for showering at work, and compensating for a slightly longer commute. If you compare the amount of time you'd spend driving to a gym, working out, then driving somewhere else, it's a no-brainer, bike commuting kills two birds with one stone and saves you gas money. Or you can try what I did for a while and get up even earlier to bike to the gym, workout, shower, then bike to work, using the cycling as warmup and cool down for the gym workout.