I've taken my bike on Ryanair flights quite a few times now. despite them getting more expensive every time (it really isn't a budget airline anymore) and in general hating the cheapo flair and the tiny seats, my bike was always fine and transport never a problem.
i always use a cardboard box that i scheme from halfords, make sure rear derailleur isn't in an uncomfy position once the bike's in and use rolls of duct tape as spacers between the box and the brake discs. chuck all your bike clothes in a bag into the box too, but i think the weight limit is 15kg now for bike boxes which doesnt give you a lot of leeway really.
have also tried lufthansa and can recommend them, bike usually flies for free there, you actually have legroom, and going to austria with them you should have a couple of destination airports to choose from (may have to do a topover though).