Though very hard to do because of visual effect and the adrenaline rush from exciting activity, I would stay anchored. However, I would continue to keep a close eye on the frequency of these bait fish schools jumping and moving.
First I would determine what kind of bait it is -- mullet, scaled sardines, ballyhoo etc. Next is to figure out why they are jumping. Mullet jumping is part of their genetic makeup, while Scaled Sardines or Threadfins are jumping because they are being chased and hunted by a predator.
But even if they are being hunted by gamefish and this is the cause of their jumping, I would still stay put. The reason is that the baitfish schools that are jumping and being hunted down are not going to stay in that area. They are fleeing for their life and there is a good chance they will come to you and your anchored boat for a few reasons. First, your anchored boat offers them protection from the gamefish chasing them. They sure are not going to sit still in the area you see them being attacked. Also the channel that you're anchored in is probably deeper water and the bait fish schools have better protection in deeper water.
Last but not least, if you do fire up your engine and slowly cruise over to the area where the baitfish are jumping, there is a good chance the predator gamefish that you are seeking to catch will feel the displacement of water from your boat moving and sound down or move out of the area. They definitely will hear and feel your boat prop and engine running and will likely move away or sound down.
If I was going to move to get a closer look, I would determine which way the tidal current was running and the wind direction. From this I would set up a drift pattern to silently move into the area while keeping all noise to a minimum. If there is no tidal current and no wind, I would do exactly what this guy in the photo I attached is doing. Swim the boat and its anglers over to the area without starting the engine. This is a very stealthy way to get it done!
By the way, your question was a really really good one!
In the photo, you can see my stealthy method for chasing baitfish schools!
Captain David M Rieumont
You can check out Captain David himself from his incredible and very popular Patriotic Angler podcasts. They cover every bit of fishing you can imagine, and there are new ones being created constantly. David and his team remain one of best resources any fishing community has anywhere in the country.