See Teddy's leg
Bungle was a character on British children's television show called Rainbow, in the mid 80's.
He was basically a fairly camp guy in brown bear suit. Thankfully, he wasn't as blatantly camp as George (a pink hippo), another character in said show.
Other characters are: Zippy, Geoffrey, and possibly Rod, Jane and Freddy.
for meaning of "bungle's finger", see synonym at "Teddy's leg".