Don't work yourself up too much thinking of world disasters. But commuting is perfectly possible with or without showers and padded shorts.

One thing, if you are worried about your seat. On my previous bike (which unfortunately got stolen during shipping when I moved), the LBS put a lock on the seat. Basically a cable that attached the seat to the bike in a way where you would need to do some serious dismantling to get it off. Made me feel safer about leaving the bike on campus at least.

No shower? a quick was in the sink works fine. You don't get that stinky from a 10 mile bike ride in fresh air. As for the bike clothes on the bus/train, I would change to a dry top if you are sweaty to avoid getting cold but other than that I would just change once I got to where I was going. My experience here is nobody cares, and I'm rarely the only one in bike-gettup on the train. Lots of people commute by bike to/from the station. Or if there are restrooms at the park'n'ride, just change there...