Both were and are great short range varmint cartridges (0-300 yards).
The Bee was originally brought out in the Win 65 Lever action. I believe it was produced to get the lever gun lovers a good high velocity varmint cartridge. This was also a big draw back as many said the rifle and cartridge was not very accurate.
It was a little faster than the Hornet and in the right rifle it was very accurate.
The biggest draw to them then and now is that they are not very loud. When compared to the 222, 223, 220 Swift, 22-250 they are down right quiet buggers. This allows them to be used to varmint hunt in more populated areas.
In the 20-60's were the hay day of wildcatting. You could buy surplus 1903, M98, 1917 for just a few dollars out of the back of magazines. Slap a heavy barrel on them and a nice stock and you had an instant varmint/ bench rest rifle.