I'm creating a story in the dying world genre, in a setting with 13th-14th century technology. One of the main characters is a woman who used to be a bowyer.
Would she have first become an apprentice?
Would she work alone, or in a workshop with other people that made items related to bowyery?
Would the purchasers of bows come to her place of work, or would her wares need to be transported to a larger town or city?
Was there a bowyer's guild, and if so, how influential was it? What did membership of the guild entail?
All accurate information is appreciated :)
Would she have first become an apprentice?
Yep, bow making was a skilled profession that took a lot of training, and a bowyer would be in need of apprentices to assist in making the bows, or just general handiwork. It's not something that you can pick up yourself without tremendous amounts of work, and apprentices are commonly mentioned when learning skilled trades of the time.
Would she work alone, or in a workshop with other people that made items related to bowyery?
Most worked in small groups, but single person operations were also used. It's just that a skilled grip could churn out a couple of warbows a day if not more at full capacity, more than someone alone could do, which makes getting large contacts easier (England for example fielded huge numbers of archers in later wars, who would all need supplying with bows). It's also worth remembering that the laws regarding Englishmen practicing weekly with bows only came around after the time period you mention, but that was an English thing after all, not Europe wide.
Would the purchasers of bows come to her place of work, or would her wares need to be transported to a larger town or city?
This is going to depend on where your character lives, and there isn't a historical consensus as it varies too greatly on location. A small village probably can't support a bowyer itself (bows wouldn't be replaced that often, though she could train as a fletcher too), so she might have a small workshop in the village then go to town, or work in a town/city itself in order to get enough traffic to support the job.
Was there a bowyer's guild, and if so, how influential was it? What did membership of the guild entail?
That's going to depends heavily on location again, and I don't know enough to answer sorry. Though I was able to find a website for a London Bowyer's guild that dates back to the 14th century, which can give some insight, but I can't speak for how widespread this was, only that this one example exists. http://www.bowyers.com/aboutUs.php
For some other sources that I could find:
http://www.medievalchronicles.com/medieval-people/medieval-tradesmen-and-merchants/medieval-bowyer-needs-images/ the main website features a lot of details that may come in handy for further reading
http://www.bowyersandfletchersguild.org/training/index.html This link details a modern guild, but lays out some of the rings an apprentice might be expected to know, which could come in handy with your story.