Is there a right time to pick the aerial bulbs off of a lilium that produces them?

When they get nice and plump toward the end of the season.

I leave them on as long as possible. You can always rig something up to catch any drops. As long as they are attached they will grow from the stem.

I picked the lower ones off mine about a month ago and planted them the same day. some have already put out roots, but mine came from a basic flower nothing special.

There is no wrong time, only that the longer you wait, the larger they get...until they drop by themselves.