I'd say - when the bulblets are ready to leave momma. When the bulb is ready for storage. Works for bulbs that produce lots of 'spawn' such as Freesia, Ixia, Oxalis.

Mostly while dormant and just before replanting because the bulbs seem to be more loosely connected at that time.

For not-bulbs such as Clivia, late summer works well for me. There's still enough growing time for the division cuts to heal and the separated plants to settle into their new pots or patch of dirt.

It could be helpful if you'd list the species you're dealing with, however.