Amanda-
My experience with Bubble tip anemonies is 4 years with 380 watt VHO. From one I have had over a dozen clones from the same one or other daughter anemonies. These were 2 years in a 55 and 2 years in a 90 gallon with the same lighting. They are doing well and reproducing, but they are not fully thriving.
I have recently upgraded my lighting to 440 watt VHO and 500 watt MH. The MH bulbs are 2-250 10,000 k Ushio bulbs. Its still to early to say what is going on in the tank, however the corals and 8 or 9 anemonies that I do have seem to be reaching and extending more than usual. I am still not at a full lighting schedual, but I think that I will only run the halides for 2 hours per day to see what changes occur.
With 360 watts like you have I would try to keep enough live rock so that your anemone could, depending on what type you will keep, can climb up to the top 1/3 of your water column, if it so chooses.
If you decide to go with a bubble tip anemone then I highly suggest you try to find one that is tank raised.
Thomas
What town in Mich you from?