Upvote:2
Two things:
Doing what you are planning to do requires two entries. You would enter Bulgaria, to rent a car, and that would void your visa. Once you cross into Romania, your visa is expired, and you can't go back to Bulgaria on a single-entry visa.
You don't mention anything about a Romanian visa. AFAIK, neither Bulgaria, nor Romania, have joined Schengen yet.
Today, the Schengen Area encompasses most EU States, except for Bulgaria, Croatia, Cyprus, Ireland, Romania and the United Kingdom. However, Bulgaria and Romania are currently in the process of joining the Schengen Area.
So as of today, you need two visas, a single-entry for Romania, and a double-entry for Bulgaria.