I think the Bugaboo is too bulky for travel...but others have and do manage it. For our 10 week old son we currently have a chameleon (on loan from a friend) and a City Mini -- bought eight years ago when our daughter was born. The latter had a great travel bag, which I could use for gate-checking in the US (not sure if it's OK for the UK).
I do think a lighter stroller/ pushchair that your baby can use at her age will be the best bet. We started travelling with our daughter from 9 weeks and had no issues at all. Just using a sling can be exhausting if slogging around a lot, and to be honest, some children don't take to them for long periods.
I can certainly attest the the City, although not super light, is very easy to use, fold and comfortable for small babies.
Enjoy the trip!
tb