I've heard that it started off with Seleucid prisoners but why did more Greeks end up coming?
Also, how many Greeks ended up going to Bactria instead of the other Diadochi during it's lifespan?
While there are a few (very dramatic) accounts of Alexander encountering Ionians who had been re-settled in Bactria and Sogdia by the Achaemenids (like in the story of the massacre of the Branchidae), Greek settlement in and the Hellenization of Bactria began with Alexander. The man spent a disproportionate amount of time reinforcing the corridor of northeastern Afghanistan/southern Tajikistan against Scythian and Iranian nomads, re-building Cyropolis as Alexandria Eschate and hiking as far as Samarkand to subdue Sogdian resistance; in fact, this is why it is speculated that ancient Iranian and Arab mythological traditions of a "wall-builder" arose, a cultural memory of various conquerors like Cyrus and Alexander erecting heavily fortified cities and garrisons in Central Asia to safeguard commerce and troop movements at that nexus of the world.
But you are correct to emphasize the role of the Seleucids -- their role in Hellenizing Bactria was crucial, because of how difficult it was to keep the region of Afghanistan under centralized rule, and how to maintain a viable Greek presence there amidst the chaos of the nomadic world. For example, many accounts describe a general revolt of 23,000 Macedonian veterans who had settled in Bactria, which was successfully quashed by the Seleucids; and for the next few generations wherein the Seleucids would rule Bactria, they would sponsor the construction, development and settlement of cities and garrisons like Ai Khanoum. The person who inscribed maxims from the Oracle of Delphi at Ai Khanoum, for example, was an Ionian who had studied at Delphi, indicating Greek civilians were migrating there during the Seleucid Era.
But the region grew wealthy as a natural result of East-West trade between the Silk Road oasis-states of western China, the Hellenistic kingdoms of the West and the Mauryan Empire of South Asia, earning the kingdom the legacy of hosting 'one thousand cities of great prosperity' (according to Roman historian Justin) and a greater penchant for independence from the fraying Seleucid Empire. It's not known exactly how many Ionian and Greek settlers settled in total during the Seleucid Era, but their armies were fairly large -- the founder of the independent Graeco-Bactrian kingdom, the rebel Euthydemus, commanded ~10,000 horsemen at the Battle of the Arius River, though some were probably Irano-Scythian mercenaries. It's important to keep in mind that like many armies in the Hellenistic world, Bactria was a polyethnic nation, with a Greek elite and a majority Iranian/native population. The phalanxes and heavy cavalry would've been staffed by Greeks, while native Indo-Iranians/Scythians would've provided the light infantry and cavalry -- especially by the time they invaded the Indus Valley in India's northwest.
The period under Seleucid rule, however, would've been the last viable time where actual Hellenic settlers would've actually come there in non-negligible numbers. The reason we have so little primary documentation of the Bactrians (from the Western perspective) is because the kingdom was cut off from the Hellenistic West by the evaporation of the Seleucid Empire by Parthian invasion; while the Parthians were 'philhellenes', they were rivals and fierce enemies of the Greco-Bactrians, as were the incoming Scythian and Kushan peoples -- which is one of the reasons the Bactrians would shift to northwestern India, founding the Indo-Greek kingdom.
Sources:
Into the Land of Bones: Alexander the Great in Afghanistan by Frank Holt
The Silk Road: A New History by Valerie Hansen