Make sure you're asking the right NPC.
Alchemists only give Alchemy BODs - not herbalists or Mages.
and ONLY Scribes (such as the ones in the two Britain libraries) give Inscription BODs - not Mages, Holy Mages, Illusionists, Necromancers, Mystics, etc.
The latter bit has what has messed up many people trying to do Inscription BODs. One would THINK that mages (who sell scrolls) would do inscription BODs, but it's actually the scribes (that only sell crafting supplies) that do.
For the various skills:
A. Tailors & Weavers have Tailor BODs - But Tailor Guildmasters don't. At one time there was a push to get Cobblers added to the bod-giver list, but nothing came of it.
B. Blacksmiths (including Guildmasters), Armorers, Weaponsmiths, and Iron Workers (in Ilshenar) have Blacksmith BODs - despite the armorers often only selling leather armor, shields, and female plate, and often being placed with the Tailor NPCs instead of the Smiths.
C. Cooks and Bakers Have Cooking BODs.
D. Fletching BODs only come from the Bowcraft/fletching NPCs, not Archers (though I believe archers can teach the skill)
E. Tinkers (as far as I know) are the only ones for Tinker BODs, though I've not tested the NPCs in Ilshenar. You would think, given the sheer amount of the BODs that are for Jewelry, that jewelers would give the BODs too, but they don't.
F. Carpentry BODs are from Carpenters, of course (and are as poorly designed as the worst aspects of Tinker and Fletcher combined). It would be nice if there were more NPCs (I can't find one in Yew, which logically should have multiple ones).
G. Alchemists are limited as above. They really need to add Herbalists to the mix.
H. Inscription is the "trick" one. You make stuff with the skill that the BOD-giving NPCs DON'T sell, and the ones that sell the completed stuff DON'T give BODs.