After watching the Sunday morning show today 7/6/08 - I also wanted to know if there was a relationship to Bing..... I Googled it and found there is no relation to Bing Crosby.
Following is a blurb from a website I found:
"Extra credit: Crosby's nickname "Bing" grew out of his childhood interest in a comic strip titled The Bingville Bugle... He attended Gonzaga University... Crosby's theme song was The Blue of the Night... He's the brother of bandleader Bob Crosby, the father of actress Mary Crosby and the grandfather of actress Denise Crosby. Mary Crosby played Kristin Shepard, the gal who shot J.R. Ewing on the TV series Dallas; Denise Crosby played Lt. Tasha Yar on Star Trek: The Next Generation... The familiy is no relation to singer David Crosby... Bing Crosby and Bob Hope both started golf tournaments; Crosby's famous pro-am was held for many years at Pebble Beach golf club in California... Crosby was the topic of the 2001 biography A Pocketful of Dreams by author Gary Giddins."
Here's the link on Bing where this blurb of text came from:
http://www.who2.com/bingcrosby.html