First, use a hoe or a rake and make a trough through the chips down the the soil. In my New BTE garden, that is down about seven inches.
I then sprinkled a layer of bone meal and spread the seeds down the trough. When I was at Buckerfields the other day I picked up a bag of Sea Soil for this planting. I then covered the seeds with about and inch of Sea Soil. I then watered which reduced the sea soil depth to about the 1/2 inch it calls for.
As the beets start to grow, you just gently push the mulch (my layers of wood chips and horse manure) into the trough little by little. Easy peasy.