Flown to Canada and US with a bike several times and no problems at all. Air Canada charge Can$50 each way for the bike and you have to pay this at check in. I always use a bike bag - the decathlon soft sided wheelie bags are good. With this arrangement, always remove the rear mech, bubble wrap it and then tape it to the frame, remove pedals and seatpost, deflate the tyres, take the bars off, also remove the QRs from the wheels. Clad the tubing in bubble wrap or pipe lagging, and use something like thin plywood down the sides of the bag to protect the frame and wheels. Takes a while to sort out but it's worth it.
Last time I flew to Canada I borrowed a hard sided bike box from a friend. These are expensive to buy (hence best if you can borrow one), but you have to dismantle much less. Just remove the wheels and bars to make it fit. The only problem I had with it was it's size. I'm such a short arse it was difficult for me to lift and manouevre so I couldn't take it on public transport, so if you're a short arse and want to go the hard sided route make sure it's got wheels. Neil Pryde boxes are good.
Hope this helps