I just asked a British friend, and he said that his understanding of the term
"bobble hat" was indeed that it meant a wool hat (ski hat, ski cap, toque,
whatever). He says that he's heard the term "bobble" meaning a wool ball.
He's also heard the term "bobbling" to mean the gradual accumulation of
little wool balls (pills, or whatever you call them) on sweaters. The term
"bobbling" may have been popularized by its use in a commercial. He says
that he's never seen any of these terms in print.