In reply to nniff:
I've done a number of transatlantic flights with a touring bicycle over the years (6 round trips since 2000), mostly with BA. I found that, if the bike is in a soft case, the handlers will treat it like just another piece of luggage, piling other pieces of luggage on top of it, slinging it around, etc. If I brought the bike up to the counter unboxed, with handlebars sideways and pedals off, the handlers were much more careful with the bike, since they could see that they were dealing with a relatively fragile object. Putting the bike in a clear plastic bag, like the one CTC sells, works just as well. If you're not comfortable with the "naked bike" approach, then I would suggest renting a hard case, or buying one and selling it on later (or renting it out a few times).
For the record, I found BA to be very reasonable about transporting bikes, both with their policies (bicycle is treated as piece of checked luggage, like Liam M said) and the way their baggage handlers treat the bikes.