The only info I could find about this is from a forum post (https://subeta.net/news/12279) from 2012. Is this the only current way, and if so, is the Queen Bea random event only available after you get access to the Blue Building?

...Or is it not an option, and I just need to rework my themed-pet-plans a bit, and just adopt a new bumbus after I get access to the building?

The easiest way would be through the Queen Bea event, but you could also change your pet into a Nostalgic Bumbus with + at Vanya and then change it to a differently colored Bumbus from there.

The would also do it, but it's a pretty pricey option for something you can change for cheap or adopt for free with Blue Building access. If you end up wanting to go the adopt-a-new-pet route instead of changing a current one, I could create a Bumbus for you c:

That's really nice of you to offer, and thank you for the info! :) I think I'll have enough money saved up to go the Vanya route pretty soon, so I'll try and use that method. It definitely shouldn't take quite as long as getting all the achievements and forum posts to unlock the Blue Building, lol.