It seems strange to me that Greeks were able to control their territories for so long, especially in the far east regions such as Bactria. How many Greeks made their way out there, was there a constant stream of Greeks emigrating east?
Not so hot on the Hellenistic period in detail. I'm better with Alexander.
Authority is a tricky thing in Central Asia and the Steppe at this time. Although many powerful tribal factions recognised the Achaemenid Kings, paid a nominal tax (varied), and may have supplied troops [Vogelsang, p222] they strongly rebuffed any direct attempts at control. Such was the case with Cyrus the Great [Herodotus, I:214].
Alexander also encountered this issue when attempting to consolidate power over his new subjects, and in attempting to access their resources [Briant, p868]. He would promote locally powerful individuals, even those whom were once enemies, like Porus in India [Q. Curtius Rufus, VII.14.45]. They would supply troops and support an influx of Hellenic peoples or Hellenism (to varying degrees), in exchange for power, riches, and external support against their own enemies. This was quite usefully employed by the Antigonids and Selucids [Khurt & Sherwin-White, p12].
Attempts to create new or more centralised hubs were met with varied success in Sogdiania-Bactria. Alexandria Eschate, the furthest Alexandria, would attempt to impose a hard border with semi-nomadic peoples who lived alongside and around the sedentary farmers in the region that is modern Afghanistan. It would embroil Alexander in nearly two years of warfare, ended when he took his first wife, Roxane, bringing the Satrapy under control [Arrian, IV. 20.4; Holt, p67-68].
This seems to have been successful in the long term as there was continued Hellenisation of Central Asia. Evidence in Ai-Khanoum, its Hellenistic features, and the stylised coinage of Euticrades I, c.150BC.
In Egypt marriage to locals wasn't perused as keenly by the Successor Ptolemaids. Instead they used the theocratic apperatus to help control the local populace whilst maintaining a well equipped Macedonian based, then Greek mercenary based, army around Thebes. They were the people who rode with Alexander, at least, to the Hellenistic and Northern Mediterranean World. To the Egyptians, they were people woven in to their local mythology over a number of years. Greek colonies were cultivated along the North African coast, such as at Cyrene. Egypt was already a trading hub, a nexus of the Med and Arabia, so the Greeks added to the entreapot. Furthermore, the Macedonian Ptolemys set about creating a bastion of Greek learning in and around Alexandria as means of garnering prestige.