Every locksmith goes through drill bits. We have to install things in metal doors, concrete, and if we are lucky, maybe wood. If you don’t know what you are doing you might break a lot of them, but as you get better at drilling you may find you are dulling them more often instead of breaking them so much.
I have lots of broken drill bits and lots of dull drill bits. You can sharpen both. It is possible to do fairly well on a bench grinder, but it is difficult to do so well that the drill bit won’t wander around when starting the hole. To get a drill bit that doesn’t skate around on metal, you need to be really really good at sharpening your bits or you need to invest in a proper machine.
Many people have invested in Drill Doctors and better over the years, but I had it on good authority from another locksmith that the Vevor model MR-20G is really good and it even sharpens carbide as it comes with a diamond wheel. (Grinding carbide is dangerous!)
As with lots of machinery manufactured in China, the directions leave a bit to be desired and are actually incorrect in spots. (To loosen the grinding wheel one should turn allen key clockwise, not counterclockwise as stated in the manual) There are excellent tutorials available on Youtube, though. This device comes with lots of different size collets to secure your drill bit properly in the machine. It has a way to fix the angle and the depth. Then you simply slide the collet holder into the machine against the grinding wheel. Rotate back and forth, then you flip the collet holder over and do the other side. At this point, the cutting edges have been established. Now you can grind away the clearance angle otherwise known as the lip relief face and create a split point. Apologies about all the jargon, I am just learning all of this today myself.
Edit: I was complaining here about this not sharpening drill bits at all, it turns out the machining on this was so precise, my collet holder was not actually rotating all the way. It works fine. It required more strength than I expected to rotate the collet holder to sharpen correctly because the collet and the collet holder had nearly the exact same diameter. That is a symptom of super precise machining! I would rather it be difficult to turn than sloppy and wiggly and easy to turn.