Hi Andy.
I know people who use bike bags regularly and don't have any problems, but from bitter personal experience, my advice is to be extra careful how you protect your bike inside the bag. The first time I flew my bike I used a bag and even with pipe-lagging round the frame tubes, padded wheel bags, bubble-wrapped bits and the whole lot inside a cardboard bike box, the baggage handlers still managed to damage my brand new £1,000 Bianchi frame! They put a dent in the seat tube. That was on the flight out from Manchester to Alicante. On the return trip, we were waiting to disembark at Manchester and I was idly looking out of a window and saw the baggage handlers get to work. They built up a big pile of suitcases on one of those baggage trolleys. The next thing, I saw my bike bag come flying out of the cargo hold and land with a thump on top of the suitcases! I would work on the assumption that they will give your bag some rough treatment and protect your bike accordingly.
A guy on the same holiday had his gear-hanger bent when his bag was dropped on one corner. He straightened it out but it then it sheared off on his first ride. After seeing that, I always now disconnect the rear derailleur from the frame, cover it in bubble-wrap and use cable ties to fix it inside the frame. I also use plastic spacers between dropouts front and rear to prevent the frame or forks being crushed. If you don't have any, your LBS will have loads of them.
BTW - if anyone is thinking of flying to the Costa Blanca I can tell you that Manchester has a huge X-ray machine which will swallow even a big SciCon bike box, no problem, and Alicante... doesn't! Every time I fly back from the Costa Blanca I have to go through the same ritual - a big security guy whose grasp of English exactly matches my zero grasp of Spanish orders me to put the box on the conveyor belt. I try using sign language to tell him that it won't fit, but he insists. Placed horizontally, the box won't go in. He stops the belt, stands the box upright, it still won't go in. He then tries feeding it in diagonally... it gets stuck! Eventually it dawns on him that it ain't gonna happen and I have to take the box off the conveyor belt and open it up. If I'm lucky, he does a quick prod about then waves the box and contents through. If I'm not, I have to unpack everything and send the contents through the machine individually. It's a right pain.