BA was quite happy to take my road bike in one of these bags. Heathrow/Amsterdam. It was even OK on the Reading/Heathrow coach. I checked beforehand by email with the coach company, BA and Heathrow.
The mechanical stuff – It is a necessary pain. – You could check with your airline, but be aware some airports have their own whims. Best to play by everybody’s rules. These usually are:-
Pedals must be turned inward (or removed to your bag).
Handlebars must be turned round so they line up with the frame.
Wheels - Keep them on - But see comment below.
A bag is required to protect other people's baggage from your (dirty?) bike.

The rest of this is my recommendations and opinions based on my experiences to September 2011.:-
If you have drop handlebars, rotate them to protect the cables, and so that the package has fewer lumps sticking out.
Wheels- leave them on if possible – while fitted they protect other parts of the bike – If removed, they may scratch the frame, and everything is more vulnerable.
Deflating tyres is a really bad idea – it risks almost certain damage during handling. The lower pressure at 50,000 feet is minimal compared to the pressure already in your tyres. (There is a technical and authentic explanation of this somewhere online). If you are worried, just let them down about 20 percent..
Protect fragile or vulnerable fittings by rotating then out of harm’s way, or removing, eg light fittings.
Rear mech - I prefer to unbolt it (one bolt), and hang it below the frame with tape. I feel it is better like that than being a sticking-out, vulnerable item.
Check airline and airport regulations for maximum dimensions. Dropping the saddle could be one way to reduce the overall height of the package. (I did notice my package was only just small enough to fit into the x-ray machine at Amsterdam.) Take the front wheel off (rather than the back) if necessary to reduce overall length.

Add a layer of gaffer tape on the outside of the bag beneath each wheel to reduce the risk of it tearing if the “package” is dragged along the ground - I saw this done to mine. Don't try cutting holes in the bottom of the bag for the wheels to spin round – They won’t!
Tape your tools to the frame (you are probably not allowed to take them in the cabin), or put them in "hold baggage".
Add a clear label, to the bag and the bike, with your name, flight details, mobile number or email address, so that the bike and you are more traceable if there is any delay.
Gaffer tape is great for securing the bag.
Allow about an hour before check-in to carry out the packaging. It is a pain, but better than a holiday spoiled by a damaged, or delayed, bike. Some airports require an earlier check in for large packages. If you're late you risk your bike being delayed.
In the week before traveling, try all your rotating, dismantling and packaging to ensure it all works.
I would do it all again exactly the same way next time I take bike by air.
It is a useful to have a paper copy of the airline’s and airports’ regulations on the subject. If necessary you can diplomatically show them to any doubtful staff. (This paid off for me when carrying a lifejacket – No I don’t cycle on water, but I do go sailing!)

I saw a cyclist at Heathrow do the pedals and handlebars, then put his mountain bike in a groundsheet. A drawstring through all the eyelets closed it up. Cheap and cheerful; but the transparent nature of the approved bag allows handlers to see what they are grasping and to handle and stow it more appropriately. Good value for money.
Go for it. Enjoy your trip.