I live in North Central Texas and have had a Bay Laurel for 35 years, mine must be male because it never had berries.
I have propagated it a few times to give to friends. I use new tip growth about 6 inches long and put it in nice loose soil.
Keep the cuttings in the shade and moist at all times, it is slow to root, sorry I didn't time mine, but I would say about 6 weeks.
I hope that helps.