This sentence is a bit misleading, because it might give the impression that this is how you designate bus lines in Hungarian, but (based on what I've been hearing in Budapest, please correct me if I'm wrong) it isn't. Instead you must use the 'es/os' suffix: "Ti a nyolcvanos buszon utaztok?" (Are you travelling on bus 80?)
You are correct! But it is "nyolcvanAs".
Here, "nyolcvanadik" implies that there are a whole bunch of buses and you travel on the one that is the eightieth in line.
So, yes, No. 1, 2, 3 etc. is:
(the ending is either "es" or "as", for everyday numbers - or "ös" for xxxx5 numbers),
and first, second, third, etc. is:
The "-as"/"-es" ending is also the short form to name bank notes:
50 - ötvenes - 50 Ft
100 - százas - 100 Ft
500 - ötszázas - 500 Ft
10000 - tízezres - 10000Ft
You are welcome. Yes, this seems to be a difficult distinction for learners of Hungarian. :)
Oh, one more place where these numbers are typically used is when talking about decades:
The seventies - a hetvenes évek
The eighties - a nyolcvanas évek
The nineties - a kilencvenes évek