The term bushido, which refers to the moral code followed by samurai. 

Their first encounter is challenging since Vivi has to involve him in fight due to her secret role as a bounty hunter.

She calls him as "Mr. Bushido" Because she misjudges zoro skills in combat.

The nickname was likely given to Zoro to make fun of his chosen style of fighting.

But even after they became friends, Vivi still calls him by Mr. Bushido.

Zoro is still remained as "Mr. Bushido" in Vivi's eyes even if she calls the other members of the crew by their original names.

Oda addressed this small mannerism in SBS, where he responds to queries from fans.

Oda said, "Once you start calling your friends with silly nicknames names, you can't really go back?"