I have used Air Transat from Toronto on European cycling trips to London, Toulouse and Frankfurt for a total of 5 flights. I just wrap my bicycle in the large plastic bags which they sell at the airport, but they have never charged me. I have found them excellent in handling bikes. Only bad experience was one bicycle (we were a group of 4) damaged flying to London but we made a claim right at the airport and were reimbursed.
I flew Transat Calgary to Amsterdam a couple of years ago. They had no plastic bags at the airport and took my bike unbagged but with pedals removed, handlebars turned and tires deflated. When I got to Amsterdam one tube was ruined from being rolled around flat and the rear tire had a bulge, I presume from rubbing against something in the hold.
Schiphol airport requires that all bicycles leaving be boxed, they sell boxes at the airport-but no tape to seal them with.
I would make sure I had a bag before hand or possibly box the bike.