I faced this problem some years ago when I had to make some parts with counterbores. I am always on a shoestring budget so I needed an economical way. This is what I came up with:
It is an index box that is partially filled with the original B&D Bullet drill bits. They have a short pilot section that provides the normal centering action of a standard bit but the remaining size of the hole is bored with cutting edges that are more or less at 90 degrees to the axis. So it can make a flat bottomed hole.
They are used in this manner: due to the odd sizes of the short pilot section of the bit, you can not use the normal procedure of drilling the clearance hole first. Instead, you use the Bullet drill first and go to the depth needed for your bolt head. Then you switch to the clearance sized drill and finish the hole.
In addition to the reversal of the order of drilling operations, there are some other differences. First, B&D (and now DeWalt) does not seem to tightly control the angle of the primary cutting edges. So some of the bits will make a flat bottom that is a bit lower at the edges and higher near the clearance hole. This is not a big consideration as most materials, even semi-hard steels, will quickly flatten out and conform to the bottom of the head of a hardened cap screw.
Another difference is that it is hard to grind this geometry with a sharp corner between those primary cutting edges and the pilot section. There will be a small radius there. You can see this more clearly in the photo below of the shop made counterbore that I made. This is not a real problem because most cap screws will have a corresponding radius between the flat bottom of the head and their shank. In many, dare I say most cases, it is even necessary to use a small countersink to relieve this area when using either a conventional counterbore or these bits.
The final difference is that you will not be able to get as close a match between the counterbore diameter and the screw head's diameter. This difference will be less than 1/32" on the diameter or less than 1/64" on each side and is hardly noticeable in the final assembly.
In all, these bits are an excellent and very economical way to produce counterbores. I have created this index of the sizes I needed for standard SHCSs at about the cost of only one or two actual counterbores.
Black & Decker no longer makes this style of drill bit. But DeWalt does still sell them. And I have had to purchase some replacements due to hard inclusions in some work.
It is also possible to create a DIY counterbore with simple techniques in the shop. I made this one using only a standard electric drill and a Dremel tool with abrasive bits. It has the advantage of having a pilot section that is actually the diameter of the clearance hole so it can be used after drilling that clearance hole. This starts with a very dull drill bit:
I took numerous readings with calipers while grinding the pilot and stopped when it was about one or two thousandths undersized to fit the pilot hole. This is the simple set-up I used:
Who needs a stinking T&C grinder anyway? Comment: That's my old bench vise. I have a much nicer one now.
