I think the second one is the correct one:P, but, what about "It's time for bed"? Does that mean the same?
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It's "go to bed." I'm a native English speaker in the United States, and I've never heard another native English speaker say, "go bed."
Both "time to go to bed" and "time for bed" are very commonly used.
I don't know why we use "to" in "go to bed" but not in "go home." English is inconsistent!