What about adding a recipe that processes raw wood, gives you wood and a really rare chance to get a wild bee or using "butterfly net" in the weapon slot while running?

Would you say that this would be a replacement for the current way to get your first queen?

An option if not replacement and it would add some more randomness.

Honestly, I don't really like the idea because it takes away from the focus of Factorio. Instead of solving logistic problems you are waiting for invisible bees.

I also have a bit of a problem with the wood process, because the first thing a player would do if they want to get into bees is create a queen. Having a difficult process to make that queen would turn people off from the mod and spam mining outposts instead.