Subjective time flows forward, the phenomenal self is embedded into this flow, an inner history unfolds. That it is why it is not a bubble, but a tunnel: There is movement in time.
Thomas MetzingerThe conscious experience of being a subject arises when a single organism learns to enslave itself.
Thomas MetzingerAs a first-order approximation, I would say that phenomenality is "availability for introspective attention": Consciousness is a property of all those mental contents to which you can in principle direct your attention.
Thomas MetzingerI believe that if we would carefully apply the distinction between transparency and opacity to the different layers of the human self-model, looking at self-consciousness in a much more careful and fine-grained manner, then we might also arrive at a new answer to your original question: What a "first-person perspective" really is.
Thomas Metzinger