The trip by bus from the city of Buenos Aires to the city of Neuquén lasts 15 hours. Yap, a bit tired, but you have the opportunity to watch the changing landscapes from the wet fertility of the pampean region to the dry and inhospitable patagonic steppe.
The ticket prices for a round trip are from 150 pesos ( u$s 52) to 220 pesos (u$s 76) depending upon the quality of the services, like lunch or dinner included, breakfast, DVD movie, beds, etc. etc.
I cannot recommend specially just one company, but there are someones with a good services like "Via Bariloche" or "El Cóndor / La estrella", departing every buses from Buenos Aires to every places of the whole country from the Main Bus Station located at Retiro neighbourhood.
Just take a taxi and say "A la Estación de Buses de Retiro por favor". That should be enough, but if you have any trouble here is the address of the Buenos Aires Main Station Bus:
Antártida Argentina y Calle 10
Telephone +54 - 11 - 4310 0700
Now I will give you the contact info of the bus company "El Condor / La Estrella"
The 1232 kilometers from Buenos Aires to Neuquén city by bus is a bit long and tired -15 hours- despite the chance to admire the changing scenery around you meanwhile the bus is moving to.
So, like always the plane is a faster option, just 1:35 hours and you will be stepping on patagonic lands.
Two main companies do it, "Aerolíneas Argentinas / Austral" and "LAN Argentina".
In the Transportation tip of "Baños de Copahue " I mentioned Aerolineas Argentinas option.
Now I'll give you the other choice: LAN
The planes are more modern -Airbus 320- and price is quite inexpensive, 790 pesos (u$s190) for a round trip.
The public transport in Neuquén is only by bus, the city isn't enough large yet (250.000 inhabitants) as to need a metro or something like this.
This public bus net is just an acceptable transport way, and we hope it achieve better standards in the future.
Anyway you can move around the city without problems and is very cheap (2,5 pesos, more or less uSs 0.80 for a round ticket), the bus net reachs every neighbourhoods and the main points of interest of the city.