Have you ever opened your case to this?!
Carpet beetles are super common, and if you have a case that is closed for any length of time, especially if you are simply storing an instrument and bows, you will be very likely to encounter them. What I think is amazing about this is that it will look like someone took a pair of scissors and cut all the hair across in the same place! If you look closely, you may see the larvae or the larvae skin that has been shed in your case.
Here is what the larvae looks like. They are tiny!
The beetles themselves are the size of the pin head or smaller. There are several different types, but the ones I see here in the St. Louis region look similar this. Remember, they are tiny, tiny! Not even close to being as big as a lady bug.
So how do you prevent them? Make sure that anything that they will like is sealed tightly. A zipper is not tight enough, nor is a normal case that is closed. You can store bows in air-tight plastic holders. You can also seal storage containers with tape. I use moth balls to repel them, but you need to be careful about children and materials that the mothballs may come into contact with. For prevention and treatment, there is a lot of great advice from The University of California's Agriculture and Natural Resources page here: http://ipm.ucanr.edu/PMG/PESTNOTES/pn7436.html