There is no acronym that is yet confirmed to stand for the name "Bing." Through focus groups, Microsoft determined that the name Bing was memorable, small, and also easy to spell. Find more details on http://en.wikipedia.org/wiki/Bing.
Bing does not stand for anything, but is an onomatopoeia, a word that imitates the sound it represents. According to Microsoft, Bing is supposed to represent the sound made during "the moment of discovery and decision making