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