According to the Robert Drew's "The End of the Bronze Age" a composite bow would take a craftsman 5-10 years to construct. This sounds like an absurdly long time to me. Wikipedia suggests that a composite bow would only take a week's worth of work.
What was it about these bows that would take so long to construct?
1 to 2 years is plenty of time for the bow to stabilise, glues to cure fully, etc. You can make one in less than a year, but if you do the final shaping of the bow (which is done after gluing the horn and sinew to the core) before the glues are fully dried/cured, then the bow can twist or otherwise deform. If you add to this time to fully dry the wood for the core, the horn, etc., and you're not in a hurry, it can easily reach 5 years (but that isn't necessary).
A yew longbow also benefits from properly seasoning the wood before making the bow. If you include this time, the time taken to make a longbow is 1-2 years. The difference with a composite bow is that you want the bow to spend time drying after glueing and before the final shaping of the bow.
The actual work that goes into the making the bow is about 1 week. Modern bowyers making composite bows using traditional tools and traditional materials (i.e., wood/bamboo, horn, sinew, traditional glues) can make over 50 bows per year (with an assistant/apprentice helping).
We (where "we" = u/Hergrim and myself) recently discussed this in https://www.reddit.com/r/AskHistorians/comments/9l9wwm/a_question_about_chinese_crossbows/
