Since people are pretty much just starting, I don't know if he's the required rank, but Duke Whitewall of The Consortium had stated he wishes to work on Weaver.
I do believe the bowstring is a fairly high weaver recipe from the information I have found.
http://ffxiv.zam.com/en/search.html?q=bowstring - Seems to be minimum level 38! That is pretty crazy if true, at least for making the Rank 8 bow. I shall just purchase a new bow from a vendor for now I suppose.
I can weave, but Im only lvl 5 with that so far... I cannot find the recipe for Linen Bow String, but if youll buy the materials, Ill meet you in Gridania, Besaid world, later tonight, and try to spin that up for you. Ive got plenty of crystals, so might just need several things of Flax? Im willing to try anyway... Im Noon Unitt.