Mortals do die, even in the blessed lands, because dying and going beyond the circles of middle earth is their gift from Illuvatar and no one can take it away, not even Gandalf. Not even all the assembled Valar! However, mortals in the blessed lands can choose the moment of their death, much as Aragorn does in the Tale of Arwen and Aragorn -- and I think in the blessed lands, they would age even more slowly than Aragorn does. So Frodo would have definitely waited for Sam and spent time with his friend, as much time as they needed, before going on. I think Bilbo would have already gone on before Sam arrived. I visualize Frodo being with Bilbo as he lies down to sleep, missing him for a while, and then-- here comes Sam down the gangplank off the last ship! It would have been a very good moment.
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