you need multiple fishing rods- basically you set one you DON'T have equipped up at the little chair looking things at premium sites, choose a bait, and then there is a certain wait time depending on the bait you used before the fish will bite. S quality baits might take 10min while C quality could take like 4 hours, but my phone sends me a notification when the fish is biting and then you just go to the premium site and hook the fish as usual when it bobs.
TLDR: you set up extra fishing rods at premium sites. don't sell off your old ones so you can use them for this. maybe even equip a cruddy rod and set up your best rod at a premium site if you are about to finish your energy pool so you have the best chance of catching whatever you set out bait for.
Fish seem random in from other sites in that level range. I've hooked one or two and had a few giant ones get away from just secret garden. ones I've got revealed for secret garden are: Leather Carp (normally Manglo River), Catfish (Manglo), Bighead Carp, and Tilapia.