Am I able to copyright a PDF form built in Livecycle and offer it as part of a billing procedure my company can resell to our product vendors? What are my rights as an author of the document?
Blank forms are not in general terms protected by copyright law. Even if the form has a lot of design flourishes, it's still considered a tool to collect data.
Some elements of the form may hold copyright in and of themselves, for example:
but the form itself is not a "creative work". The same is true of things like blank diaries, bank checks or sheets of headed notepaper.
The answer depends a lot on the country you live in and, if different, the county your users reside in. In the end, you will probably need a lawyer to get a reliable answer.