Honey, wake up, a new question just dropped:

Which came first, the bumble or the bee?

came from humbul-be and merged with Middle English bombeln

As you've said, in both senses it's related to the sound they make. "Bumble" on its own, in the sense of clumsy, meandering movement, is probably unrelated but I guess it's plausible that it also had an influence on the mutation of "humbul" to "bumble" even if the latter was primarily about the noise.