Channel catfish are not best suited to an IBC, though I raised (an killed) many catfish in an IBC. They need a bit of room to spread out. TCLynx recommends 400 gallon minimum for channel cats and I have found that to be good advice. Their pectoral fins have a sharp, saw-like bone that will pierce other fish if forced together too closely. That said, I raise up to 150 channel cats in an 800 gallon pond and they tend to cluster together when spooked.
I'm not familiar with bass, but generally speaking i would go as high as 1 lb fish per 5 gallons of water, as long as you have adequate bio filtration. I'm not sure why you only have 9" of wet media in a 14" deep bed, but that limits your bio filtration significantly. Assuming you are using IBC grow beds, and you have wet media within an inch or two of the total depth, that would be enough to support about 35 fish with 175 gallons of water. As they reach 1lb. average then you will need to harvest a few to keep the stocking density manageable.
Things crash very quickly in a high density situation. If you lose pump circulation all your fish will suffocate within a couple of hours. It's very important to have supplemental aeration, and plans for a power outage (backup battery or similar) with high stocking density.
BTW, kudos for fish-less cycling. Well done. But be aware this only establishes a base line bacteria colony. You will likely experience a large ammonia spike, followed by a large nitrite spike. So be very aware and test water daily after adding the new fish. Do not feed them for 24 hours, then keep a close eye on ammonia and nitrite when you do.
I strongly recommend adding salt at 1-2 ppt to protect against nitrite poisoning. Other benefits of salt are most freshwater pathogens do not tolerate salt well and it helps protect your fish from many parasites, infections and diseases. For metric, add 1KG salt for 1000L of water for 1.0 ppt. For imperial measurements: 1 gal water = 8.34 lbs. 175 gallons (FT) + 150 gal (sump) = 325 gallons x 8.34 = 2710 lbs. of water. 2710 x .001 = 2.71 lbs of salt for 1ppt.
USE A SCALE TO WEIGH THE SALT. DO NOT use table salt. For nitrite protection this must be chloride salt like sodium or potassium (not epsom salt). Pool salt, aquarium salt (expensive) and water softener salt are good sources. Be sure you get it without any additives like anti-scale or anti-rust. Do not use table salt (has iodine). Solar salt (sodium chloride) or Potassium chloride from Home Depot are good. You should get a refractometer for accurate measurement of the concentration (~$20)
I hope you already have some plants in place too. Good luck and enjoy the journey.
Some things to watch out for:
Drains clog with roots and beds overflow
Power goes out and you don't have a notification or backup power
(I use smart switches, they can notify you when the power is out / lose connectivity for 30 minutes or more)
ammonia / nitrite spike
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800 gal sys 2016IBC sand-ponics system 2021, 3 IBC GBs
9 kW Solar Electric 2011 - Upgraded to 12 kW 2019
"Aquaponics...solar-powered nanotechnology that produces fresh vegetables and meat, while purifying water..." - Rick Op, Houston Texas.