Moss needs three things to thrive. High soil acidity, low soil fertility, and excess soil moisture. The first two issue are easily corrected with application of lime and nitrogen. That usually mitigates the third issue. Properly applied both are safe to use around your bees.
Lime for lawns (different from that for roof treatment) can be purchased everywhere in fast acting powdered form, and a slow release granular form. I find the granular to be more appropriate for homeowners, using an inexpensive handheld broadcast spreader. Easier to get even coverage without over applying. Wait a couple of weeks and you will see the moss turning black. Rake it up and dispose, then seed and fertilize with readily available “lawn food”. If you have a large lawn, consider renting a power rake for a couple of hours.