Similar to other celebrities' phone numbers, Justin Bieber's number is unavailable because it is an unlisted number. Celebrities often ask their telephone providers to not publish their number to a public directory.
In fact, anyone can ask for his number to be unlisted. Politicians, lawyers, doctors and other public workers usually opt to remain unlisted. The practice of requesting unlisted numbers stems from a tendency by the general public to harass publicly visible figures by frequently calling.
If a person wants to make his number private, he can contact his phone company's technical support department. Most companies charge a small fee for this service.