I'll start of this post by stating up front that I've purchase bitcoin, but I've done so with no intention of actually spending it.
I've purchased it because of the wild fluctuations means that it has the potential to be a wonderfully performing investment, or a dire one. In some ways a bit like gambling, except it's not all over in an instant because it's red and I've bet on black.
Now with that in mind, Airlines are already a fickle business. They say the fastest way to become a millionaire in the airline game is to start off as a billionaire. So if they started accepting bitcoin their healthy balance sheets could turn from wonderful to we're declaring bankruptcy, to we're just sold the most expensive economy fare ever, to go home everyone, we have no money left all before lunchtime.
Bitcoin needs to stabilize (although please not before I've made enough to retire to my own private island) before it can really be considered a viable currency.