There's nothing new about using masking tape on a bit to indicate drilling depth, but it can be difficult to tell when that tape sleeve hits the workpiece. And if you go a little too far, the sleeve tends to slide up the bit, making subsequent holes too deep. Rather than simply wrapping the tape around the bit like a sleeve, stick the loose ends together to form a flag. When the flapping flag wipes away all the sawdust around the hole, you've hit your depth mark.
Try this if your drill bit is short enough (or your screws long enough): Mount your bit in the drill chuck so the length showing measures slightly longer than the length of your screw. This makes it nearly impossible to drill too deep because the chuck jaws prevent it. However, those jaws can mar your workpiece, so stop just short of the jaws touching the wood.
Tip #3: Stop collars provide the ultimate solution
For a few dollars' investment, stop collars give you a can't-fail means of repeatedly drilling to a predetermined depth. Slide the collar onto the bit, then tighten the setscrew(s) securely against the outside surfaces of the flutes (not inside the flutes or on their cutting edges). Be warned: Steel stop collars, although priced attractively, can mar your wood surface. Instead, try SlipStop collars, shown in photo. A nylon boot allows the stainless-steel collar to spin within it, preventing wood damage.