Hi CJ,
Welcome to the forums

I'm so jealous you are off to Argentina!
How much time do you have for your trip? That might help with the bus or plane advice. I travelled everywhere by bus, and the buses in Argentina are great. You also get different types of seats, the most expensive recline right back like a bed.
From BA it's about 14 hours to Mendoza or 18 hours to Iguazu by bus. Going direct by bus from Mendoza to Iguazu, it's about 36 hours, so if you have time and were going to do that, it might be better to go via Córdoba or Salta then across.
Bus companies are
FlechaBus but the website is in Spanish;
Crucero del Norte;
Andesmar All the prices are in Argentinean money.
If you are just going 3 places, it doesn't make much difference which way you go, but I'd recommend taking the local bus across to the Brazilian side of the falls too - it's close, and the local bus is very cheap, though you might want to check your visa situation for Brazil depending on where you are from.
I'm afraid I can't help you regarding flights - I'm not even sure of the airport codes you've used, sorry.
Let us know how long you're going for, as that will likely help the advice you get.
Cheers
Kathryn