<p>Is it possible to print toothbrush bristles using a common FDM 3D printer? I am particularly interested in the width of bristles, closeness together of each bristle, and the flexibility of each particular bristle.</p>

Actually last year a group did use a normal FDM printer to 3d print hair, brushed, etc. See the press release from Carnegie Mellon University
https://www.engadget.com/2015/10/29/3d-printing-hair-is-as-easy-as-using-a-hot-glue-gun/
http://technabob.com/blog/wp-content/uploads/2015/11/3d_printed_hair_by_Gierad_Laput_Xiang_Chen_Chris_Harrison_1.jpg
That said as far as I know you will not have access to this process, and is probably under a mountain of patents and other innovation killers.
Now how to do this outside of fancy software.
For a FDM printer the smallest nozzle I ever got was 0.1mm, it jammed instantly. One could print rows at this precision.
Now we have to move to something more advanced, such as DLP. Not the materials you want, but closer to the size you want. a formlabs can print at 25 microns. Which as a hair is 17 microns, you are "close enough" .. but a resin would be brittle and break. They do have other materials such as flexibles, but I am not familiar with them enough.
Also just going to mention. Tiny slivers of plastic is more likely to cut you than comb you.