When heavy rod fishing, you should bring your rod, your knife, and 25 fishing bait or feathers, go to the fishing spots and catch a full inventory of fish and cut them into fish offcuts and caviar/roe. If your inventory gets full of offcuts and roe/caviar, drop the fish offcuts and continue fishing/cutting using the caviar/roe.
You can pick up the offcuts after you have used up the caviar/roe as they are also bait. Dropping the caviar/roe takes more time to drop than the stackable offcuts. This gets you around 50 to 60k an hour at 70 fishing.
Note that it is possible to run out of bait just from cutting open the fish so bring some back up bait/feathers to be on the safe side. When fishing with Bait, feathers, offcuts and caviar/roe in your inventory you will use the bait first, then the feathers, then the offcuts, then the caviar/roe. If you are banking the caviar/roe for barbarian potions it is a good idea to take plenty of bait/feathers to start with and bank the fish offcuts with the caviar/roe. This way you can save the offcuts for later barbarian fishing trips so that you won't have to bother using other bait or feathers.