The simplest and most cost effective option is to pop to your local bike store and ask them for a bike box that is no longer in use. Ensure to wrap your bike in bubble wrap, especially where there may be touch points between your wheels and the frame.
There are also plenty modern, bike specific hard cases and soft bags designed specially for travelling with your bike. These may vary in size and protective material. If you have a high value carbon bike, we suggest going with a hard case option and to make travel even easier, choose a case that has durable wheels on it.
If your bike has disc brakes, we suggest that you remove your disc rotors to prevent them from getting bent and insert a brake block between you disc brake callipers.