I'm not sure what the current take is on the gravitational 'Instant action at a distance' idea, but I think the current speed of Gravity is regarded as being that of light. I don't think Gravity is instant, so I would agree that there must be a 'Speed of Gravity' one way or the other.
mass cannot warp space, if that were so, we would warp the space around our bodies and have a gravity of our own
We do indeed warp space around our bodies, and we do have gravity of our own. The only difference is, a human being has an extremely small mass, and therefore has a correspondingly small gravitational pull - so small that it is generally unnoticable. The same goes for every single object on the planet. Mountains have a larger gravitational pull, a postage stamp would have a much smaller effect still. The earth on the other hand, is a very large mass, and has a correspondingly larger and very noticeable gravitational pull.