I followed the lead of a poster on another WW forum with a jig to get the holes started straight as well as to set the spacing from hole to hole. I used a corded drill and a 3/4” brad point bit from Lee Valley which is pretty long. His jig was just a thick block of wood with a hole drilled thru then mounted to scrap ply or MDF with attached fence to set the spacing from the edge. I did mine a bit differently with 2 blocks mounted on MDF the full bench width and 2 more holes thru the MDF with the same hole-to-hole spacing and offset from the drilling block holes the distance between the rows that I wanted. Then I just kept inserting dowels thru the extra holes into the ones I just drilled and kept moving the jig down the bench. If you go that route, setup of the jig hole spacing and offsets are critical. I had to pitch the first one when 3-4 test rows on scrap ply showed me I was starting to steer off from parallel to the edge. Once the holes are drilled as deep as you can go, the remaining depth can be done without the drilling guide blocks and jig.
-- Use the fence Luke