I want to build a jig to speed up production of a furniture item. The jig will hold a piece steady while the user hand-drills a hole in a certain spot. I want to use a steel bushing to guide the drill bit so that the hole is straight. The bushing will be 3/4" long with a 1/4" ID, for guiding a 1/4" bit. My question is, will this be damaging to the bit? I'm thinking that the cutting is done with the point, which never touches the bushing, and the flutes that do touch it just collect the waste, so it would be okay. What do you say?
This is fine and commonly done in industry. The "sides" of the drill bit, more precisely the margin of the flute land is not designed to cut, but rather to clear chips from the sides of the hole and prevent the bit from binding in the hole. The margin is ground at an angle very close to tangential (and often not ground at all).
Drill bushings are a standard tool and die component:
available for example here: https://www.zoro.com/value-brand-drill-bushing-type-h-drill-size-h-h326hp/i/G3097355/
They are generally made from hardened steel, to withstand repeated use without excessive wear. They are often pressed into a tool plate or jig at the desired hole position.
If your application only called for a small number of uses, regular steel (e.g. 1018 cold-rolled steel) might serve just fine. But if it's for production use, a purchased item will likely be better and more economical than what you can produce yourself.
Note that a drill bushing for a 1/4" drill may not be precisely 0.250" internal diameter. In this case, perhaps 0.252" is more appropriate. A bushing hole with insufficient clearance will cause excessive drill margin wear. A purchased item will have thought all that through for you.
There are other considerations when using drill bushings, like where the chips go and so on. Here's one resource with some discussion on that. Many others are easily found on search now that you have the right technical term :)