Hi Ian,
I don't know if my experiences will help you (airports and carriers are so variable over time and as a result of world events), but I used the original factory box when flying with from Oregon to Amsterdam and back. I was careful to pad everything with sleeves made of old socks and blocks of foam, and was careful to insert a spacing block between the fork blades and to detach and zip-tie the rear derailleur to the chainstay. Front fender was detached and sleeved over the rear, saddle and attached seatpost were carefully secured. Foam pipe insulation on all the frame tubes, crank arms, etc. Nothing rattled, and lifted in and out as a cohesive unit. I took the further precaution of photographing the bike and taping a print of the photo inside the box in several places so the inspectors could readily re-crate it in the event of an inspection. I think one thing that really helped was placing crush-protectors in the center of the frame to keep the box sides from being driven inward. I've had good luck using some made from the safety caps used to cover re-bar ends at construction site concrete pours. I've also found heavy corrugated cardboard taped into triangles and set endwise do as good a job keeping the box sides apart.
On the way over, my luggage was fully disassembled and searched. The bike was passed through with only a look-see inside the top flaps.
The return trip was a different story. My luggage wasn't inspected, but the bike...was. Somewhere, probably on arrival at PDX (Portland, OR), the bike was uncrated and whoever tried to put it back had no idea how to do so, but that didn't stop 'em trying. The pedals were driven through the spokes, taking out several and bending the hub flanges and damaging the rims. The Brooks saddle was badly scarred, the paint marred in a number of places. The hub quick-releases were disassembled and rattling in the box, and it was a mess throughout, with fenders buckled and not a mark on the box, so I know it wasn't done in transit or by the baggage handlers. The TSA (Transportation Security Administration) left a card inside the box indicating it had been selected for special inspection. It took forever to get the bike at PDX, and for the longest time it could not be found. I feared it had been lost. When I arrived home to find the damage and called to report it, I was told there was no recourse, since the TSA is immune to damage claims, and it was out of the airline's hands, and so wasn't covered by traveler's insurance. This was in the late summer-early fall of 2008, when there were concerns over shoe- and underwear bombers on flights and possible explosives hidden or disguised in other items of luggage, so this may account for the extra-rigorous inspection.
Cost me a pair of rebuilt wheels (new hubs, spokes, rims), a lot of touch-up paint, a new front rack set, and new fenders.
On arrival in the NL, I stayed at a friend's apartment outside Rotterdam, so collected and re-used the box for my return trip. When I inquired about the availability of boxes there in case mine hadn't been up to the task, I was informed my 60cm road frame and 700C wheels were too big for the MTB boxes generally available at local shops, so that's something to keep in mind if your bike doesn't have 26" wheels or is a large frame for 26" wheels. My bike wouldn't have fit in the racing-bike cartons they had, either. When curiosity caused me to inquire at Schiphol Airport as to what most tourists did, I was told they discarded their boxes outside the airport on arrival, and then returned the departure desks with their bikes freshly boxed. I was told the KLM desk had boxes for sale, so this might have been the source. It was a handful to juggle the crated bike and my luggage by myself on the hand cart available there. It would have been a lot easier if I'd thought to include a bungee or two to strap things to the airport luggage cart.
I think wrapping the bike in plastic or a "bicycle bag" alone would be risky, but I understand this is fairly common practice at Indian airports. On the other hand, it would surely make inspection easier, and might avoid that kind of damage. I took my own box each way, but before I left, the local/stateside representatives of my destination carriers were amazingly helpful, even placing calls for me to determine if boxes were available at my planned destination, and told me who to contact at the service desk overseas. One offered to leave a note with my name and expected date of departure with the overseas airport desk clerk once my plans were finalized, all to make sure a box would be available if needed. I'm not sure if it would really work out that way, but it might be worth a try if you need a box for your return and aren't sure where to get one.
Best,
Dan.