In a bumblebee you have two genes: spider and pastel. A queen bee is that plus lesser/butter. Spider, pastel, and lesser/butter are all 50/50 chance at getting passed on. The only way to get 100% offspring of the same gene (like all pastels) is to have a homozygous (also known as super in the herp world) parent. There are no known super spiders. Spider is a dominant gene, when it gets passed on and you only have a 50/50 shot at it getting passed on.

When pairing a bumblebee to a lesser/butter you'd need to hit the 50/50 odds on all those genes to get a queen bee. You'd have a 1/8 shot at a queenbee.