The research has actually been done. For the experiment, groups of lawn owning households in Massachusetts were instructed to mow their lawns at one-, two-, or three-week intervals. As one might suspect, lawns always seem to have some flowering plants in them, such as clovers. Lawns mowed every two weeks supported 30 percent more bees than did the other lawns. Mowing every week eliminated nectar sources, and three-week interval mowing—maybe a little too lazy, resulted in grass too tall for the bees to access the flowers.
Biological Conservation Volume 221:160-174