It's an irrational fear. You won't be able to convince her. Get a professional occupational therapist who has experience with eating disorders

Pheobe, is right, I would have a therapist weigh in on the subject. in the mean time address that Fear, What can Bones do to you? What do you think will happen if you eat a bone? Has someone at school teased her about her food. ( This happened to my daughter she has a bologna sandwich and a friend told Jenna Bologna has germs and she freeked.. Kids take things literally so I think Investigate where the thought process began . There is always a reason for behaviors = Always..and if she has never behaved this way or been leary about her food I suspect some one may have planted a funky seed in her head that is possible.. Has she seen anything that would have provoked this obsession? example, does Dad in the family hunt ? Investigate. and then also ask her if she is having any other visions, hallucinations. constipation issues and Sleep issues will bring on such strange obsessions as well. Good luck

Could she help you prepare the food to witness that there are no bones in her food?

I had a friend who's child developed extreme anxiety about eating after he had a minor choking incident. It quickly spiraled out if control and he required over a year of intensive feeding therapy with a specialist.
I don't say this to frighten you but if it were me, I would address it with a professional quickly before it gets worse.

An occupational therapist could help. They teach kids how to enjoy and have fun with their food. Do this ASAP. You are probably mirroring the anxiety watching her not eat.