Yes, it works, and I had a friend that did it that way, and it took time, but was not a big drag.
BUT they are working on the subway, and so you are going to have to drag your luggage around more (unless they are done – they might be).
They are running surface busses that mirror the subway exactly as they are working on a few stations, which included the Metro at the train station when I was there a month ago.
Also, make sure you know how to work the system – buy a ticket, get on, punch it. The “kontroll” officers are famously ugly, and I got to see a bit of it – you don’t want someone shouting at you that you need to pay a $500 fine right now or go to jail.
I pretty much walked everywhere that I needed to go in Budapest so, unfortunately, I don’t have much experience with the transit system.
However, I did get on a cacble car once thinking that I could just buy a ticket at the next stop (I couldn’t find a machine where I got on). This was a bad idea. Two “kontrol” officers asked me for a ticket and when I didn’t have one, they showed me a ticket that said “Fine : 200 Euros”. All I had was about 70 Euros and some Forints on me which they took and made me get off immediately.
I asked my husband about this (he’s from Budapest)… He says there is a direct train to the Ferihegyi Airport, but he’s not sure exactly where you get on, and also unsure how much it would cost in comparison. But either way he agreed that M2+M3+Repter Bus would work just fine.
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