I think you could ride the carbon bike, or the mountain bike. If you choose the MTB, you should get some slick road tires which will improve the commute a lot. Personally, I have a few bikes and depending on my mood I might take one or the other. If I want to go fast and light, I have a racy bike for that. If I want to carry stuff and be more mellow, I have a tour-ish bike. You could try using both bikes for variety and to see which you like better on your particular commute. Since you can take the bike inside I don't think there's a big risk of theft. I wouldn't be too worried about the bus rack. Just sit in the front and watch.