This is a (long) acronym for best friend who is my best friend's friend. This is often used as a pet name for someone you don't really know that well, but is a really good friend of one of your own really close friends.
Carol: You know, I liked that girl you introduced me to yesterday very much.
Maria: Who, Theresa? She's like, my very best bud!
Carol: In that case, Theresa is my bfwimbff.
Maria: Who, Theresa? She's like, my very best bud!
Carol: In that case, Theresa is my bfwimbff.
by Evelyn Norre June 7, 2009