The story of the word bumblebee is curious, but (contra Mr. Burns of the Simpsons) certainly doesn't lead back to a form like bumbled bee, in the way that ice cream leads back to iced cream, or the American form skim milk descends from the form skimmed milk still current elsewhere. The bee part is transparent, and there is a Middle English verb bomb(e)len, meaning to make a humming sound, presumably of imitative origin. So there you are.
However, it's clear that the older form was humble-bee, where hum(b)le is an intensive of hum, which is also presumably of imitative origin. Whether bumblebee is a new coinage based on bombelen, or whether it is an alteration of humble-bee by dissimilation, or a mixture of both, it's impossible to say.
But when we look in Pokorny's etymological dictionary of Indo-European for hum, we see it under the root kem²-, as expected by Grimm's Law, and with Lithuanian reflexes in k- and Slavic ones in ch- that also refer to humming noises and bees. That certainly does not sound imitative to me -- the sharp sound of [k] is nothing like a bee hum, which has no beginning and no end. So in the end the obvious imitative nature of bumblebee leads to a riddle wrapped in a mystery inside an enigma.
And there remains at least one dangling oddity: Pokorny also lists an Old Persian -- at least I think that's what "Ai." means -- reflex meaning "yak". Yaks grunt (as the Linnaean name Bos grunniens indicates), they don't hum, and what is Old Persian doing with an inherited word for "yak" anyhow? English, like most modern languages, has borrowed its word from Tibetan.