The Minecraft Wiki states that bee nests generated by growing Oak or Birch trees within 2 blocks of a flower will contain 1-3 bees. I successfully used this mechanic to generate a bee nest with a bee in it on a server, while in 1.15. Then the server updated to 1.16, and I tried again with the same method. I generated 4 more be nests and none of them had any bees in them.

I since went into a Creative testing world and the first bee nest I generated using this method had 3 bees inside. Theories include:

Dependant on y-level (testing world was Classic Superflat)
Dependant on biome (the only biome used on the server were mushroom fields and ocean)
Random chance to not get the bug
Dependant on number of flowers (in the test, there were 2 flowers within 2 blocks of the   successful nest)
Dependant on distance (in the test, one of the flowers was directly adjacent to the sapling)

I used Oak trees both on the server and in the testing world so Birch trees may be fine.

Also I should note, the bee nests that generated with no bees still made the "Bees work" sound effect. After getting bored of waiting for them to come out, my friend and I broke the nest (without Silk Touch) and no bees came out.