So I would do the same thing that the mobile phone does. I would track the position of your controller (in your case rotation also) and calculate delta distance/rotation and if it is bigger then threshold then I would cast the rod.
Or you can add physically simulated rope with the bait to the end of the rod and every frame calculate the force that the bait is being pulled from the rod because of centrifugal forces (maybe you don’t have to calculate it, it probably is somewhere stored). This can be easily calculated from the length of the rope and velocity of the bait. This technique will be probably best, cause it is physically accurate and you can just release the physics constrain when you want to cast the rod. The bait should fly out as IRL.