In enginnerd talk: how much deflection do I need to apply to get to plastic deformation? There are tons of variables here, but is it .010", or more like .100"? Just looking for a conservative starting point.
Don't go enginerd on it. That's coming from an ME, for what it's worth.
First, unbreech it and read the light rings to discover exactly where and how much the bore is curved.
Ignore the outside of the barrel, it is meaningless because all gun drills wander a bit and any barrel which has not been straightened the old fashioned way relative to the bore will have deviations, some of them egregious.
To straighten the bore, you will need a sturdy bar or workbench, some wooden blocks, a big C-clamp or ball joint press, and a 1" dial indicator and stand. Place your blocks equidistant from the apex of the bend and your clamp ON the apex of the bend. If the bend doesn't coincide with a flat, use angle blocks or shims or notch the blocks appropriately to rotate the barrel as required to attack the bend exactly on its plane. Depending on barrel material, length of curved bore, and wall thickness it might take 1/8" of deflection to reach the elastic limit or it might take 3". Likely much less than 3" but I had a 20-gauge barrel with a hook just past center and again near the end in a slightly different direction and the middle one required an unbelievable amount of movement to reach the plastic point. Bend on it and release, measure the result. If nothing, repeat in, say, 50 thousandths increments until it does. It doesn't take long. When you begin to see some permanent results via your indicator not returning quite to zero, take the barrel loose and read the light rings again. Repeat until the bore is straight.
Clean up the crown and go shooting. If it's still misbehaving, repeat the bending until it isn't. There's no way you'll collapse that barrel unless you block it on the ends and drive over it with a truck. A thin shotgun barrel is a different story, especially if you don't use shaped blocks with a lot of surface area to distribute the stress.