Sadly, I don't know how to change the thread title. You are saying to make a drill guide to keep a bit centered? Could this be made from aluminum or would that be too soft and need to be mild steel. Also how much difference between guide hole and size of bit. Would 1/4" be a good size to try?
QT:[Would 1/4" be a good size to try? 1/4" what? end mill? I guess that would be Ok
The bushing should be .003 smaller than existing hole
(X) Aluminum would be too soft,
CRS would be OK, any steel Ok, drill rod and you could harden with it with water quench.
.003 clearance would be OK as you dont want the bushing stuck, or the cutter stuck.
Cutter flatten the broken bolt or put a centered dimple in it. Feed the cutter slowly to not break it, as Stephen said avoid carbide if the bolt is
file-soft. Still take care with a nibble feed rate because you don't want a broken HSS cutter in the problem.
Getting the center then you might drill all the way through and fill it with WD or the like for a few days soaking.
With the broken not becoming lose and having some still good thread at the top of the hole, you might drill the broken bolt out to near the hole wall diameter ..and then go in with a tap.
*Oh you don't want the guide bushing to spin out of control and wreck the top of the hole, so put on a wrench flat..or a vise grip on it so not to spin. You can deliberately turn the guide bushing by quartes to maintain the ID from the effect of any bushing cutter wear.
*Sounds like Stephen is suggesting to just carefully (slow feed) come straight down with an end mill to square off the top of the broken bolt...That should work with no problem. Perhaps a 1/4" or 3/8" end mill and a slow down feed.