Disclaimer: I do not own a billing company, but I have worked for several in the past, and currently have worked for one for the last 8 years.
Most of them are/were LLC's. The one I currently work is an LLC, and has both an attorney and an accountant. While I don't know of any "rule" or "regulation" that says you NEED an attorney or an accountant, I think having both is smart/good practice. You just never know what may happen that will require one or the other, or both.
The only other thing I can suggest is that you absolutely SHOULD have E&O insurance. I don't know if that is what you mean by saying you have received a quote from Hiscox, or not.