As bad as I hate to post this, my experience with Chihuahuas and bees are not good ones! My mother had a small Chihuahua that died from being stung one time....it was a direct hit to one eye and the dog went into shock...the end.
The dog was always barking at something and was not really close to the hives....but for some reason, the guard bees did not like the barking sound and went right after her. Before that, she had never bothered the bees other than snapping at one that was too close to her.
Again, my parents are elderly now and have another Chihuahua.....this dog's bark seems to be a bee magnet....as they head right towards the sound. My bees as a rule are not agressive, as they are gentle Carnies....the Italians get ticked off first and then they all go after this poor dog!
My cats can be sitting right on top of the hives and not get bothered at all....thus, I believe it has something to do with the sound or pitch of the bark.
A fence might or might not be the answer, as my bees go towards the sound of the barking dog.