Because the "Y chromosome" has nothing to do with sex determination in bees. Instead, the number of X chromosomes determines the sex. With only one X chromosome, the egg will develop into a male. This is called a haplodiploid system of sex determination (the male bees are haploid, having only half the number of chromosomes).
EDIT: I should add that there are many systems of sex determination, not just XY or the haplodiploid system. See the Z-W system (males are ZZ and females are ZW), the X0 system (the males are diploid for all but the sex chromosome), and temperature-dependent system of sex determination.
The Cape honey bee in South Africa can create female offspring without the queen being mated. Female stick insects can also produce female offspring without males, all daughters will however be clones of the mother. I guess this is a last resort to ensure survival in difficult times until a male is found to mate with.