I used to travel a lot with my mountain bikes. Sometimes up to 15 times a year. Still fly a few times a year now but only with Air Canada. I just use one of their old clear plastic bag bike bags from the early 2000's. Does BA allow them in a bag or do they have to be boxed? I have it down to an art using pipe insulation for padding and zip ties. I just remove the front wheel,pedals and handlebars and turn the fork to the right and lower the seat. None of my expensive mountain bikes have ever been damaged in 25 years of packing them that way and that includes once when one was lost and had to be flown on a tiny prop plane to Moab from Denver. The advantage of this way over hard cases and boxes is that you don't have to have a massive rental vehicle to carry the case/box at the destination