I am going to go out on a limb here and challenge one of the real experts here (that's a tip of my hat to cthegame who probably knows more than I do). But, in my experience, some anemones can survive well in a new setup. If the tank is mature enought to house corals, it will probably be mature enough to handle a bubble tip anemone. I have started new tanks in this hobby three times, and each time I start wtih a clown and and anemone. (This allows me to introduce the clown to the anemone, and allows me to wait to see where that darn anemone wants to stay, so it does not travel around the tank killing corals as it snuggles in). In all three instances the clown and the BTA did very well.
That said, cthegame is absolutely correct that the lighting in your tank is not sufficient. I blast 400W MH's at my bubble tip and it still strains towared the surface trying to soak in the rays. cthegame is also correct that a dead anemone is likely to take the tank with it when it goes. It may be a good time to upgrade those lights.