Actually a drill press can be pretty handy for this - I did the dog
holes on a 2' x 6' x 2 3/4" maple top I picked up a while back.
Pondered on how to get it up onto my dril press table, then realized
that I could work on the floor instead. Put a 2 x 6 under each end of
the bench top (clamped to the top) so it would clear the base of the
drill press (I used a nice old Delta Homecraft benchtop I have, but
could have done the same with my floor mounted drill press - in either
case you will have to take the table off, and lower the head down
close to the floor). I used a 3/4" brad point drill and got nice
clean holes (I did back them up with a board to prevent tear out when
the drill came through). Just kept sliding the bench top along and
getting each hole centered - the weight of the top kept it from moving
once I started drilling. If you could not drill deep enough, the hole
you have started will serve as a guide to finishing it with a brace
and auger bit - again, you will need to back up the hole to prevent
tear out. In any case bringing the drill press to the work this way
provided a good solution - not too obvious to me at first, but once
the light went on, I think there are other places where it will be
helpful.

Stephen