Check with the airline for how much it would cost. It's probably on their website somewhere. $400 sounds expensive, but my experience has been all within the US, and I was also a very high-status frequent flyer the times I travelled with a bike, so often I got away with oversize and/or overweight baggage for free. And then there's the altermative: they might soak you for $1,000 or more when you show up at the airport with your bike, so if you can't find out on the web site, call the airline. And then hope you get someone competent on the phone. Because what they tell you over the phone won't be binding on the airline's agent at the airport.
And what are you going to pack it in? That won't be free, either. If you want the bike to survive, you're looking at something substantial. A normal bike shipping box probably isn't substantial enough.
You'd probably be better off selling your bike, and taking the proceeds from that sale along with the money you'd save by not flying with your bike and buying a new bike.
If you really want to keep the bike, look into just shipping it separately via an international shipper.