FWIW, healthy Ulva has a "holdfast", so it should ideally be attached to the rock. I don't know how the plant differentiates, but perhaps you can get it to grow "roots" or a holdfast by attaching it to rock (that's where mine grows). You might also be able to plant a tip of it in the sand, but, I don't know.
Like Mike_Noren said above, Ulva likes bright light, and grows fast (IME). This is the first time I've seen or heard of Ulva growing under flourescent bulbs, but, I have limited experience with Ulva.