I flew to Sri Lanka with my bike a few years ago for touring. However, I own a Bike Friday which packs into a suitcase. I had no problems even though I had to fly on 3 different airlines to get there from the USA. BTW, I left the empty suitcase at a guesthouse in Negombo (just north of the airport) while I was touring. There are companies which will ship your luggage ahead of time, including FedEx, however they charge a fortune. Luggageforward.com is another outfit.

As for Sri Lanka, I loved the country. It's a great place to visit. However, the cycling varied enormously. In some areas, the roads and touring were great. Elsewhere, the roads were awful. In one region (area north of Negombo), the bus drivers were homicidal, and cyclists were expected to go off the road when a bus coming in the other direction was passing another vehicle. Buses were always passing other vehicles.

Make sure you visit Sigiriya, and biking in that area was very nice.
The descent from Ella Gap to the south coast was fantastic. Biking in the mountains was very nice, but not the road from Kandy south into the mountains. The train is useful to get into the mountains from near Kandy.
I avoided biking between Galle & Colombo because of heavy traffic. I took the train, and it was easy to put my bike on the train.