I haven’t seen any figures supporting that - do you have a citation?

https://ourworldindata.org/travel-carbon-footprint has data from 2022 for passenger-kilometers in the UK:

    Domestic flight 246 g
    Diesel car 171 g
    Petrol car 170 g
    Short-haul flight 151 g
    Long-haul flight 148 g
    Motorbike 114 g
    Bus (average) 97 g
    Bus (local London) 79 g
    Plug-in hybrid 68 g
    Electric car 47 g
    National rail 35 g
    Tram 29 g
    London Underground 28 g
    Coach (bus) 27 g
    Ferry (foot passenger) 19 g
    Eurostar (to Paris) 4 g

So the only way that could be true would be if the bus was significantly emptier than the plane so the same emissions were amortized over an order of magnitude fewer passengers.

Moreover, this ignores the future: there’s a straightforward path to electrifying a bus which has been deployed in production for years but no proven alternative for planes.

If the airplanes are completely full (which, despite all attempts by Ryanair to scare away their customers, they apparently still are). But this fails to account for "induced demand": if flights would be more expensive or less convenient, people wouldn't fly on weekend trips/holidays, visiting relatives in faraway countries etc. as frequently as they do now.

It's the first time I hear about that. Do you by any chance have more information? Or keywords where I can find more?

I don’t regularly take buses to the other side of Europe to eat some gelato and gawk at cathedrals for a weekend. A lot of people use cheap airlines as cheap entertainment.

Possible, but taking the bus halfway around the world would also produce a lot of emissions.