I have to add that the barrel may not be bent, but may have run-out.
For those who do not know, runout exists where the barrel boring did not run exactly down the center of the piece of barrel material. In other words, the hole in one end is centered in the blank, but it is not centered on the other end. The bored hole is aiming to a slightly different spot than the outside of the barrel.
Most good barrel makers stamp their information on the flat of the barrel intended to be placed at the bottom under the wood when the rifle is done. This is done so that any run-out is oriented up and down. Not right and left. The sight height easily accounts for up-down runout. Left and right run-out can have you end up with the sights hanging off the barrel flat on top. Some barrel makers produce barrels with no run-out, and scrap the defective ones.
I bought a decent handmade .45 Lancaster flinter to learn on as my first gun. It grouped fine, but the sights hung off the barrel like you said. The barrel was not marked (maybe Dixie Gun Works), and apparently the builder did not know how to check for run-out. Bummer for sure. It may be one that would benefit from barrel bending.
The idea passed to me for bending a barrel scientifically was to place it on a 2x4 block under each end of the barrel on a strong bench. Clamp the ends with C-clamps. Use a big C-clamp in the center (with appropriate bearing block of wood on top), and screw it down until you flex the barrel as much as needed considering spring-back. You can measure in the center from the bench to the barrel with a caliper. Pretty simple, but repeatable.
Another thing to remember is to always pack the dickens out of a barrel when shipping for any reason. One barrel I received from the stand-up maker Rice ended up bent somehow in transit. It is a very thin .50 Southern Classic profile. Someone in the USPS must have jumped up and down on it, or dropped a heavy box on it. Jason made me a new one of the same profile. Thank you Jason.
I hope this helps someone. I am no expert. Best wishes, and God Bless, Marc