Freelancer would mean he doesn't have only one employer, and instead takes jobs from wherever he finds them.
For example:
A freelance carpenter takes woodworking jobs from any individual soliciting his work.
A freelance journalist writes articles and gives them to whatever news source pays him for those articles.
A freelance translator translates whatever article anyone pays his to translate, it could be a business or an individual.
An entrepreneur is one who makes a career out of starting their own businesses. If this man owning the bookstore started it by himself (didn't buy it from anyone else) he is in fact technically an entrepreneur. However, in practical use, an entrepreneur is one who starts their own businesses (more than one).
For example, Joe is an entreprenuer, he started a bookstore, sold it, then started a web design company. Or Joe started one bookstore, it did so well that he then decided to open a second book store. The emphasis is that he shows "enterprise" and is constantly trying to improve himself economically by means of the creation of businesses.
I don't like businessman, it's very vague and general. Bookseller sounds a little weird and will just prompt several follow up questions. I also don't like self-employed, to me it's more similar to freelancer than anyting else. It is also a little vague and will prompt questions.
So, then what to call himself?
In legal talk, sole propietor would be the correct title. The communly used version of this, and my recommendation, would be a small business owner. If you wanted to be a little more specific you could say, I own a bookstore or I own my own business.