I think most experienced reefers will tell you that you're going to have to actively battle aiptasia. Left alone, they will eventually take over the tank, either slowly if you don't feed all that much, or very rapidly if you use coral foods.
I've beaten an infestation back many times over the last 20-30 years. As others have noted, using Aiptasia-X and similar products tends to cause the dying adults to generate planulae larvae that scatter all over your tank. My early successful solution was actually taking the tank down and storing the live rock in circulating heated saltwater in the dark for a few months. Obviously, that's not a desirable solution because of the work that it takes and the absence of the tank, but it's 100% effective without having to bleach the rock.
For me, aiptasia-eating fish was a hit and miss solution. As others noted, getting a fish that prefers aiptasia, even among species known to feed on them, was quite variable. And that's not an option in a relatively small tank - a copperband is going to feel pretty cramped in a 3' long tank.
This solution is going to sound tired, but the best cure is prevention, and that's quarantining everything that goes into the tank, including snails. And the quarantine needs to be long enough for small aiptasia to grow to visible size - I typically go for 6 weeks while feeding coral foods that encourage aiptasia's growth.
Once they're in a reef tank, my best success without the afore-mentioned tank teardown is aiptasia-eating nudibranchs (Berghia species). Unlike fish, this particular organism is aiptasia-specific; it can't survive without aiptasia, and it will eat nothing else, so there's no concern that it will eat coral. You can get them from various sources; my latest purchase was from Reeftown - they were shipped quickly, and were in excellent shape. Highly recommended.