This quote demonstrates that libertarianism and anarchism is not a refusal to accept authority. Rather, it is that authority must not be assumed but consented to by an individual’s initiative. In particular, Bakunin consents to authority on the premise that is reasonable to do so. In other words, he can find a justification himself for why a specific person should have authority over him.
The reference to a special person also indicates that it is a rareity that a person will exist who is deserving of being consented to have authority by another person. To have authority over another is a special treat that needs to be earned, rather than be assumed that is justified.