The references we have to Greeks in Bactria prior to Alexander are considered unreliable. I'm not going to claim that they're wrong, but it will make for a more clearly accurate answer if I leave aside those claims for now.

In Bactria itself, at the time that the satrapy declared independence with its own king, we can be sure that there was a substantial but primarily urban population of Greeks. In the parts of the Hellenistic world where Greeks were settled into existing or new cities, we tend to find that their different origins blend together, only hinted at by the presence of particular personal names. This is the case in Bactria- we might be able to guess a particular person was descended from Thracian Greeks or Achaean Greeks by their name but by little else. The Seleucids attracted Greek colonists of all sorts to their colonies, so the Greeks in Bactria probably descended from all different parts of the Greek world.

There would have been a Persian presence in Bactria at the time of its conquest, we know from the few satrapal records we have access to that it had Persian governors. What we can't be sure of is how long a distinctly Persian presence remainded in Bactria, because we can't really distinguish Bactrian and Persian personal names at this time; they're all being rendered in Aramaic or Greek, which tends to obviate some of the elements you'd use to tell the difference.

The Bactrians themselves are rather central to the story of Bactria. The assumption remains that the majority of rural dwellers and artisans in Bactria would have been native Bactrians, who were speakers of an Eastern Iranian language rather than the Persians who spoke a Western Iranian language. The differences between Bactrian and Old Persian languages would not have have been as enormous as, say, the present day difference between Pashto and Farsi, but they would have still been distinct. We lack some crucial context for the Bactrians, in that we don't know what was politically and culturally going on there in any detail before the Achaemenids conquered the area and formed a satrapy. One could assume that satrapies tended to reflect large existing entities absorbed by the Empire, but that doesn't reflect all of the Achaemenid satrapies we're aware of, and some assume instead there was some kind of large kingdom covering Bactria and a host of nearby regions like Sogdiana, Margiana and Parthia. I should also mention the Sogdians here- in much later periods they were highly active across Central Asia as merchants and we know a great deal about their culture as of the 6th-9th centuries AD, but in the Greco-Bactrian period we don't even know if/when Sogdiana was included in Bactria or controlled by it, only really knowing for sure that it seemed to be more of a meeting point of settled and nomadic peoples than Bactria.

There would have been a presence of 'Scythians' as well, by which I mean nomadic peoples from deeper into Central Asia. The Greco-Bactrian state employed them as soldiers/mercenaries, and it's likely the Seleucids had been before that. It's difficult to say exactly how deep that presence was, Bactria was heavily reliant on cavalry but to my knowledge we don't know enough about land-usage in that period across Bactria to say how many areas might have been given over to horse grazing. The best known areas are Balkh, site of ancient Bactra, and Ai Khanoum, where there was a French led excavation and a survey of the surrounding landscape, but Bactria is a landscape of oases and human engineered alluvial farmlands surrounded by desert, what goes for one specific area doesn't necessarily apply everywhere.

We don't really know about movement of Indian people into Bactria, only objects, but it's not unreasonable to assume that the military expeditions into India let to some unwilling migration of Indians in a state of slavery to Bactria itself. The political centralisation of Bactria seems to have disintegrated into civil war shortly after those expeditions, and it was never re-united under a single Greek authority after that point. This is when they start talking about Indo-Greek kings, because there's a load of Greek ruled statelets across parts of the Indus region and nearby. We know King Menander as a historical reality from his coinage, which are something of a bridge between Indian and Hellenistic designs, and he's also referred to in some histories from antiquity where they assert he controlled part of Bactria as well as cities in 'India' like Taxila. But we can't really conclude from such little evidence what if any movement of Indians into Bactria that would have led to. We also have to reckon with 'Indian' being a pretty loose term in this period, in the modern day there's quite pronounced differences between Indian cultures and the subcontinent was no less diverse 2200 years ago or so. Indeed, a lot of 'ancient' definitions of India include what we'd now consider part of Pakistan.

We should also touch on the fact that across the Hellenistic period in Bactria there was a growing cultural fusion between Greek and 'Iranian' cultures, which adds to the complexity of talking about 'Greek' and 'Bactrian/Persian' culture. These were Greeks increasingly comfortable with Iranian imagery and local deities, and Bactrians who at times were writing with the Greek alphabet and adopting Greek visual styles.