I allow a bowyer to craft arrowheads, if he has the time and materials. The problem is that arrowheads are metal. Even a master blacksmith can't work metal unless he has a forge, and some metal to start with. (Tools are necessary too, but they come in the Artisan's Tookit from the PHB, which your bowyer probably has already.)
It's possible to set up a workable forge in the wilderness, but it's not exactly a fast operation. For simplicity's sake, I say it takes two hours to set up and get hot, and then you can make up to 20 arrowheads in a regular day. Raw material is more problematic, but I allow any nonmagical weapons to be reforged into arrowheads.
Alternately, if you're about to leave town for an extended adventure, you can buy a bunch of premade arrowheads. They're far easier to carry than an equivalent number of arrows.
Once you have the heads, you can make shafts one at a time. If you've got an hour to kill, you can make one shaft; spending a full day (8 hours), you can make 10.