There's been a number of threads recently on bike bags and flying with your bike and I think I have some ideas.
1) Carry a large 4 or 6 mil thick clear plastic bag with you. These are often called contractor or demo bags This does double duty as an emergency tarp and can be used to put the bag in if necessary on trains and buses. A strap attached to the bike will let you carry it easily. In an emergency you can use it to put the bike on a plane too.
2) If you feel safer with a proper bike bag I'd go with a soft bag or as light a hard case as you can find as the baggage weight limits keep coming down. On international flights it seems to be 23kg and many hard cases weigh over half that allowance themselves. Soft bags range from 2kgs up to 8kg. You can also use a bike box that you discard when you arrive, but they can be cumbersome and then you have to get another one on the way back
3) Now that you've decided on your bike bag what do you do when you get to your destination? Well there are some options.
a) If you stay in a hotel on the first night they'll probably keep it safe for you until you get back. If you are leaving form another airport you can post it to your final hotel.
b) Most airports have left luggage so you can just stash the bag there if you'll be leaving from the same airport. However, this can get expensive. at London Heathrow it'ss about $10 a day.
c) Finally here's the best option. Use General Delivery or Poste Restante in Europe. Simply mail the bag to yourself at a post office on your route. They will hold it for you for between 2 and 4 weeks. If you have a longer trip planned just do this multiple times to post offices along your route.
As an example I plan to go to the UK this spring and I'll pack my bike and most of my gear in a soft bag keeping it under 23kg and it will go on as one item of luggage, the allowance is 2 items. My handle bar bag will be my hand luggage.
There is a post office at Heathrow so I'll post the bike bag to myself at that post office addressed like this
"my real name"
They will hold the bag for 2 weeks and it will cost $20. If I was going on a longer trip, say a month, I'd post the bag to myself at a post office half way along my route, collect it and immediately post it back to Heathrow. Total cost $40. The cost of left luggage for a month would be $160.
The large plastic bag will be used if I have to use a train of to protect the inside of a car etc.