second-hand advice
Hi, I had what I thought might be aptasia, but turned out not to be, but I got some advice from an expert in these things in the meantime which I'll share with you. I hope you find it helpful.
He said that if you think it is, you want to get rid of it in a way that won't disturb it, because sometimes they will release spores and suddenly you'll have them all over your tank. He suggested a couple of ways:
1: peppermint shrimps - they love aptasia, although if you have other small anemones growing and want to keep them the shrimps would go after them too.
2: put coral glue on it, completely covering it.
I'm really glad what I have didn't turn out to be, as he went on to explain what nasty little buggers these guys are.
Good luck!
PS. Of course there is always a small possibility that it could be a baby anemone like my Bartholomea Annulata, but since it isn't hiding it's base under a rock, it probably isn't.