If you remove the collet and insert the bit so it is flush with the bottom, this is the minimum depth. Mark the shaft with sharpie and use it as a guide.
Not having the collet fully engaged on the shaft increase the danger of the bit coming loose.
With the collet installed and the bit fully inserted, this is the maximum inserted depth ...... which should be avoided
to prevent the bit from sticking in the collet. Typically, 1/16" up from the full depth is enough to prevent a seizure when the collet is installed. Some router bits have a rounded shoulder at the intersection of the shank and if fully inserted, will bind in the collet. So, that's why you pull it back out a 1/6" or so.....
The OP's question was about the minimum amount of shaft length inserted which will hold the bit securely. There is very little info online about this question. Some sites say 80% , others say 75%, other say no less than 1" ... except this:
Try to find the shank dimension of a router bit ...... I couldn't, not On Freud's site or MCLS's site. I gave up. I may just go to the shop and measure a bunch of my bits ...... now I'm curious.
OK, my 1/2" bits standard length, measure about 1 3/8" of shank. The 1/4" bits measure about 1 1/8" of shank. So, given the 1" recommendation, there's not much extra length, maybe 1/4". Given the 3/4" dimension, about 1/2" extra length.