virgin currently will take 23kg of bike box/bag for free – used to be 32
“proper” bike cases are pretty heavy and you may not get down to that
If it’s a full sus you may be able to halve the frame relatively easily and get it into a big suitcase surrounded by clothes, then put wheels & fork etc in some kind of box with some foam packing
I’ve done a variety of the above for about 8 years now and no breakages (but one 14kg bike case has been FUBAR in that time – bike inside was undamaged though)
I haven’t tried it (yet – not had the bottle) but you could probably just put a big clear plastic bag over the bike, take off the spiky bits and rely on the handlers to recognise that it can’t have a hundred bags stacked on top of it