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Is that my bike?

I'm not sure if the simple subject is that or bike.

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In this specific case, that would be the subject. In 'Is that a bike?', there is ambiguity -- either that or bike could be the subject, depending on what is intended. – Kris Oct 1 '12 at 5:54
@Kris, no, that isn't quite correct. The article plays no part in determining the subject in your example. You would differentiate between a specific or general bike, but the subject is always 'that'. "That is a bike." "Is that a bike?" For example. Maybe you could clarify? – Adam Oct 1 '12 at 8:07
@Adam cf. Bill Franke below. – Kris Oct 1 '12 at 10:47

The grammatical subject is the demonstrative pronoun that: That is my bike. To turn the statement into a Yes–No question, subject–verb inversion is the usual rule: ⇒ Is that my bike? But That is my bike? with a rising tone is also a Yes–No question.

That comes before the verb and is the subject of is.

The logical subject is bike because that's what the sentence is about: the bike.

That is a pronoun that replaces bike in this sentence.

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It looks to me like "is" operates symmetrically here, just stating that the two sides are equal. "That is my bike" is the same, with each word playing precisely the same grammatical role, as "My bike is that". – David Schwartz Oct 1 '12 at 10:26
They can't play the same grammatical role. One has to be the grammatical subject and the other the subject complement. Change the positions of that and my bike and the sentence you get should become My bike is that one. Semantically they're the same, yes. A simpler example: John is my brother = My brother is John. Same meaning but different grammatical subjects and different focus and they answer two different questions: Who is John? and Who is your brother?. – user21497 Oct 1 '12 at 10:43
Either answer can be given to either question. They do play the same grammatical role even if you think they can't. Here, "is" functions like an equal sign, stating that the two subjects are equivalent. Which one you choose to call the "grammatical subject" is arbitrary. "Who is your brother?" is equally well answered by "John is my brother" as it is by "My brother is John". – David Schwartz Oct 1 '12 at 10:55
@david: You'll have to document that claim. It's like saying two different 3D bodies can simultaneously occupy the same space. I know theoretical physics makes strange claims; I'm not aware of that one. Do you also claim that John, my brother, is the policeman has three simultaneous grammatical subjects even though linguists might label the 1st a grammatical subject, the 2nd a noun in apposition, & the 3rd a subject complement? While any one can be the grammatical subject, position seems to determine which one is which. Why else different names but for different functions? – user21497 Oct 1 '12 at 11:59
@david: Perhaps "equally well answered" in speech, but formally, John is my brother is the correct answer. Does "End with" = "With end"? – user21497 Oct 1 '12 at 12:01

It should be that. Let's consider the following example:

That is his bike.

Now if you remove that, the setence becomes:

*is his bike. And you are left wondering what bike is his

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And you are left wondering who the bike belongs to” is wrong or irrelevant: the bike is “his” for both of your example seNtences. – jwpat7 Oct 1 '12 at 7:37
@jwpat7: you are right. Fixed it. – Noah Oct 1 '12 at 10:24

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