I had been recently discussing with another club member the trials and travails of aiptasia. They'd volunteered to cycle some rock for me, but also wound up with an aiptasia outbreak, and commented they'd never run a system that didn't eventually get it.
I was thinking, well, with my clean start and no live rock, maybe I could avoid it, but, from what I can tell, unless you add very little to your tank and get very lucky, you're almost certain to get it eventually.
If you don't have anything that would prey on them, Berghia are probably your best bet, or a Peppermint Shrimp, if you can get one that is known for sure to eat it - ideally, both. Problem with Berghia is that it dies out once the aiptasia is gone, and in smaller systems or with smaller numbers of them, they may not get the last of it before they die out. Between a few Berghia and a Peppermint, you've got a pretty decent chance of controlling or even eradicating it, IF you can keep it out of your filter system.