I do see flights as low as $176, on July 6 for example, one-way on Malev Hungarian Airlines—nonstop—if booked from consolidator CheapOAir.com. This includes taxes and fees and is the cheapest flight I see between Hungary and Montenegro (BUD to TGD, specifically).

There is one direct train from Belgrade to Podgorica. It leaves Belgrade at 13.10 and should arrive in Podgorica at 21.54; for train composition see vagonweb.cz
The train ride is very spectacular, see for example this video.
There are also several buses to Podgorica from Belgrade or Sarajevo.

There are also direct coaches from Prague/Bratislava to Bar, which also stop at Budapest. They are coupled in the EuroCity No. 345 “Avala” (Prague-Belgrade), leaving Budapest Keleti at 13:00, arriving to Bar the next day at 8:42 in the morning. These direct coaches run only from today till September 17.

Or you can travel with one transfer, use any train to Belgrade and change to a train to Bar.

Return ticket should be under €150 with discounts if more than one person is going.

ONLY ONE???

My search engine shows at least 4 pairs of trains. The four direct trains from SRB to MN are here:
Category, Number, Departure Belgrade, arrival Podgorica, arrival Bar, Note
InterCity, 431, 10:10, 18:52. 20:09
InterCity, 433, 13:10, 21:54, 22:57
night train, 435, 22:10, 6:49, 7:53
night train, 1343, 23:10, 8:25, 9:37, runs June 11 to Sept. 11 except Sunday/Monday nights

Also, when looking for a flight, try TIVAT airport as a destination, much closer to the sea (at sea level) than Podgorica. There are charter flights there from Vienna (Austrian Airlines) and from Prague (Travel Service), but probably also from Budapest.

And yes, it should be a bit cheaper than Croatian coast. And it is in fact very beautiful, especially the area of Boka Kotorska Bay and Budva.

Thanks Dacia, After watching the video I want to travel this route. Trying to find fare prices but i’m running into some language barrier. I am american and ,yes, Unfortunately I only speak one tongue.