Probably a good idea. It's the ref that appears on route maps, and the name's almost internal. Plus, it sorts better in lists :)

Maybe it's better capitalised as "Bus Airline REF: Wherever → Somewhere Else" though?

I think Wikipedia would probably capitalise it as "The Airline" or just "Airline" if they had a page for it https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Trademarks. They suggest looking at independent texts to gather consensus for lowercase brands. Looking around, the Oxford Mail doesn't include the definite article when talking about the route: https://www.oxfordmail.co.uk/news/19302677.oxford-bus-companys-airline-service-steps-frequency-travellers/