in antiquity... Cf. the following interesting passus from Strabo (1,2,1):
"Indeed, the spread of the empires of the Romans and of the Parthians has presented to geographers of to‑day a considerable addition to our empirical knowledge of geography, just as did the campaign of Alexander to geographers of earlier times, as Eratosthenes points out. For Alexander
p51opened up for us geographers a great part of Asia and all the northern part of Europe as far as the Ister
River; the Romans have made known all the western part of Europe as far as the River Albis (which divides Germany into two parts), and that regions beyond the Ister as far as the Tyras River; and Mithridates, surnamed Eupator, and his generals have made known the regions beyond the Tyras as far as Lake Maeotis and the line of coast that ends at Colchis; and, again, the Parthians have increased our knowledge in regard
to Hyrcania and Bactriana, and in regard to the Scythians who live north of Hyrcania and Bactriana, all of which countries were but imperfectly known to the earlier geographers. I therefore may have something more to say than my predecessors."
Information about the Bastarnae would thus have (partly) come from those historians who wrote about the campaigns of the Romans near the Danube, and from those who wrote about the exploits of Mithradates in the north. Posidonius, Apollodorus, and Hypsicrates come to mind (all of them mentioned and quoted by Strabo). I suspect that Hypsicrates might also have been his source for Burebista.
Another point: Torsten has usefully pointed to a passage of Plutarch which identifies the time of Mithradates' campaign against the Bastarnae:
I would suggest that another passage from Strabo (7,4,3) with my proposed emendation, refers to that campaign:
"This city [Chersonesos in the Crimea GK] was at first self-governing, but when it was sacked by the barbarians it was forced to choose Mithridates Eupator as protector. He was then leading an army against the barbarians who lived beyond the isthmus as far as the Borysthenes and the Adrias; this, however, was preparatory to a campaign against the Romans."
1. Read "Tyras" instead of "Adrias"
2. Strabo has telescoped information from a number of Pontic campaigns in the north. We know, for instance, that the military help provided to Chersonesos against the Scythians occurred much earlier, after the death of Skilur (Skiluros) c. 112 (who had been responsible for the "sack" i.e. the conquest of Chersonesos holdings in the northern Crimea), when his son Palak was Scythian King. Mithradates' general was Diophantes, and at that time Chersonesos retained its full political autonomy. Cf. the decree on Diophantos at
http://www.chersonesos.org/?p=museum_coll_ep1&l=eng
(interesting as a major source for political events north of the Black Sea in the last decade of the 2nd c. BCE).
3. So it is in connection with the Bastarnian (and Sarmatian? These would have been the Iazyges) campaign that Chersonesos was more closely integrated into the Pontic Empire acc. to Strabo. Perhaps the campaign was undertaken to relieve Bastarnian and Iazygian pressure against Tyras and Olbia. The general in that campaign was perhaps Neoptolemus (cf. the reference to the "tower of Neoptolemus" near Tyras in Strabo). Just possibly, this Neoptolemus (well known in Appianus' work) would have been a junior general in Diophantos' army when he battled "the barbarians" near Panticapeum on two occasions (Strabo 7,3,18). These "barbarians" might either have been Scythians supporting Saumak the Scythian at the time of the original acquisition of Bosporus by Mithradates (cf. Diophantes decree), or some other tribal units of Bosporus who did not like the Peirisades disposition of the kingdom in favour of the Pontic ruler. But that's
just a guess.