Generally, the majority of bone products are made from Cow bone, which is processed for use in musical instruments, jewelry carving and other crafting uses. Bone "blanks" can be purchased in a variety of sizes. It is also possible to clean and dry bones yourself for project work.
It is fairly easy to work with bone.
Bone can be cut with a fine toothed saw such as a hacksaw. It can be sanded and filed, and some artists use grinding stones and wheels on it. You have to be careful not to let the work get too hot as you can burn it. Finishing can be done with fine sanding and abrasive polish.
Although strong, bone can be brittle, so you wouldn't want to make the pick leading edge too thin. A steeper taper more like a "jazz" pick would likely be more resistant to chipping.
Ivory and Tortoise shell were common materials for plectrums (picks) before plastics.
You will get some tone differences from the different materials, and flexibility and wear rates differ. Bone is hard and picks made from it don't have flexibility so are more like stone or glass picks.
To get started all you need is a saw, a rough file and some sandpaper, and a bone blank big enough for the size pick you want.