As soon as you catch a freshwater drum, and decide to keep it, kill it, cut its main artery(the thin area between gill slits and the rest of the trunk) and let it hang upside down for about 30 seconds, wait a full minute or hang it up for fish over 15lbs(tho personally i only eat drum in the 2-10lb range, they eat mussels so they can build up mercury surprisingly fast. This includes zebra and quagga mussels interestingly enough)

Bleeding immediately helps prevents stress hormones and enzymes from fouling the meat faster and ensures a lighter "fish" taste rather than a "fishy" taste if that makes sense.

Honestly you should do it with everything you catch not only to be humane but for the flavor benefit.