Why does there have to be a category AdvP? McCawley suggests in The Syntactic Phenomena of English that an adverb is a modifier of anything other than a noun (for which we have the special term "adjective"). So lets just use "adverb" in that way, as a term of convenience. Then for your example "I'll go to bed in an hour", if the sentence structure makes "in an hour" a modifier of "go to bed", "in an hour" is an adverb, according to the definition, but its category in the sentence structure is PP (or P-bar). If you want to reserve the term "adverb" for lexical adverbs like "immediately", we can call "in an hour" an "adverbial" instead of "adverb".
There might be a case for a category Adverb-bar, for a phrase whose head is a lexical adverb.
There is a neat characterization of "modifier" that emerges from McCawley's analyses, but which he doesn't state explicitly. A "modifier" is something that is appended to a constituent of some category to create another constituent of the same category. So "in an hour" will be a modifier of "go to bed", which let's say is a VP, if we assign the structure:
[VP [VP go to bed ] [PP in an hour ] ]
"Modifier" is another term of convenience which need not be a category that turns up in sentence structure.
Added: I see that I didn't get around to answering the question. Any head whatsoever -- that's the answer, so far as what I said above goes. I've placed no constraint on what a modifier can be (though there might be such constraints), so anything that could be the head of something could be the head of an adverbial phrase.