The redstone machine looks like this (you may also see the following image):

.L..R..O→O↓

.A..B..D..N.

A=air, B=any solid block, D=dispenser, L=redstone light, N=bee nest, O=observer, R=redstone dust

And the effect looks like another image.

After a bee put honey in a nest, causing a block state update, the machine starts squirting honey bottles and the nests' states switch between honey_level 0 and 5.

I also did another experiment and that indicates that when a nest(in any honey_level) is in front of a dispenser consists of empty bottles, the dispenser will "collect" honey from nest and also may shoot it out.