The FAQ tells me it's only possible to acquire a Bumble, or transform an existing pet into one, via an area of the site I'm not allowed into.

Ordinarily, I'd just be patient and wait until I qualify for that place, but I already have a large number of items for my Bumble and they're really starting to pad out my inventory. I need to either abandon the idea of having one for quite a while (and get rid of all the items), or ask someone else to acquire a Bumble for me.

EDIT: Thanks Prussia, I lov my bee <3

I could make you a common one, send me an smail with the name you want and whether you want it male, female, or genderless, unless someone's beaten me to it ;)