Just stay away from gig bags and get a hard case. I have what USED to be a nice solid top Dean guitar ($500 a few years ago- not high end but now too low end either) that now has two nice cracks in the top and some dings because I didn't bother to buy a hard case for it, like an idiot. My next nice guitar will come with a hard case. If it goes on a bike, it'll be with an xtracycle or a bob trailer and be well tied down. If I were going to do it regularly, I'd modify the case to fit on a rack like a pannier.

Hope this helps!