as deva say there isnt direct option from the baneasa airport !
"Do you recommend bus or train"
the problem is that the train rute from bucharest to giurgiu [romanian city border] are under constraction therefor the train make long way.
and the train that deva mention are :
A . rapid 463 that go from bucharest to Thessaloniki and pass Gorna Oryachovitsa dep' 12:16 and arr' to gorna at 17:19.
B . rapid 383 that go from bucharest to sofia and also pass Gorna Oryachovitsa dep' 20:04 and arr' to gorna at 01:31.
"1. How to get from the airport to the Train/Bus Station"
from baneasa airport you have bus 780 that go direct to bucharest gara de nord train station.
to take this bus go out from the terminal pass the main road bucharest ploiesti and there you have the station and also place to buy a ticket that will cost you 3.5 lei one way.
Frequency [depart from otopeni airport] :
http://www.ratb.ro/download/trasee/780FLUVIULUI.pdf
another bus are bus nr' 205 to take him you go as mention to bus 780 and when you are at the ather side of the road jast walk sout to the intersaction lass then 100 meter and you will found the station, one way tickets cost 1.30 lei.
Frequency [depart not far from strand straulesti]
http://www.ratb.ro/download/trasee/205STRANDSTRAULESTI.pdf
map of the public bus transportation:
http://www.ratb.ro/download/harti/autobuze.pdf
for bus bucharest-bulgaria :
take the bus nr' 783 that his station are jast where the 780 bus location.
tickets cost 3.5 lei for one way.
you take the bus and get off at the last station called [piata unirii] .
then walk left lass 50 meter till the corner and tern right and you see hotel horoscop
from this location the bus left you see schedule at this link :
http://www.autogari.ro/Transport/Bucuresti-Ruse/643-14550.aspx?lang=UK
the price are not show but I remember that was 40 lei + - .