Forget putting painters tape on the bit, and having to carefully monitor the depth. I have ~100 holes to drill, without breaking through my desktop from underneath for mounting Multiboard.

These are collars for smaller drill bits, one for up to 1/16, and another for up to 1/8". Print it out, probably will want to do a brim so that it doesn't fall over during printing. Adjust the depth of the bit in the chuck.