There's no need to worry about any type of bike being damaged or excessively worn just from being on the rack. And carbon isn't nearly as frail as some people would have you think.

No matter which bike you take, you'll want to sit in front, and keep an eye on it every time the bus stops. I'll never forget the day, a few years before I owned a bike myself, that I guy I knew came and sat in the back of the bus with me. At a stop, someone else snatched the bike and rode off before he could even get off the bus to chase.