Small drills often bend and can be easily straightened by hand while chucked. But a 1/2" would be a lot harder to straighten this way.
I would look at the shank to see if there are any raised burrs on it. The shanks of many drills are soft while the tips are hardened and when they slip in the chuck the hardened chuck jaws often raise these burrs. These burrs can cause it to be mounted at an angle and appear bent.
If there are any, you can grind them off or even use sandpaper to remove them. You would need to be careful to keep the basic shank on the same center line.
OTOH, if the bit is really bent, a strip of sandpaper could also be used to take some off of one side of the shank. Clamp the bit in the vise with the shank sticking out to one side and use the sandpaper like a shoe shine cloth on the high side. Use some wood or soft metal scraps to grip it and prevent damage to the flutes. This could take a bit of effort and frequent tests.
As for testing, if you are using a chuck/drill to judge, be sure that the chuck is true. Check it out with several other bits first.
Make it fit.
You can't win and there is a penalty for trying!