What made some states acquire standing armies and maintain regular bureaucracies during the 6th century BCE?

Legitimization of raids on neighboring states.

Brahmanas began composing Sanskrit texts known as the Dharmasutras. These laid down norms for rulers (as well as for other social categories), who were ideally expected to be Kshatriyas. Rulers were advised to collect taxes and tribute from cultivators, traders and artisans. Were resources also procured from pastoralists and forest peoples? We do not really know. What we do know is that raids on neighboring states were recognized as a legitimate means of acquiring wealth.
Gradually, some states acquired standing armies and maintained regular bureaucracies. Others continued to depend on the militia, recruited, more often than not, from the peasantry.