blocking a bee sting with a shield will make the bee continuously try to sting you

— "If the player deflects a bee's attack with a shield, the bee continues attacking until it succeeds in hitting the player"

Quoted from the wiki. I assume since it's mentioned there, it's probably a feature (though it might be best to hear from a higher-up to confirm, the wiki can be wrong). Makes sense to me; a stinger wouldn't necessarily pierce into a shield and thus be removed from the bee, so it could continuously attempt to sting.

then if a shield can deflect an axe, why can it pull a bee's stinger off?

I'm not sure exactly what the logic is behind it, but I think it's working as it's intended right now, so it's not a bug. You could make a suggestion in the suggestion forum though.

Is this still an issue in 1.16.4?