If I was getting the Hexamid Solo, I would get the beak. The weight is negligible and it rolls up, out of the way. I don't think you would need a bivy with the Hexamid tent (that is, with the mesh walls + floor, which I think you are talking about). I would, however, take a bivy if I was just getting the tarp. For either tarp or tent, I would take a polycro groundsheet, even if it just stayed in the pack during nice weather.
If I was getting the Hex Solo Plus, I would still think about the beak, but could go either way.