Of course her bush is going to be hairy (contain hair) otherwise it wouldn’t be a bush.
Its autological.
Actually, "autological" means "possessing the property it describes. The word polysyllabic is autological, but the word monosyllabic is not. Because the word short is in fact short, it is considered autological." (Wictionary)
If one were to say that her bush is hairy, that would be tautological.
Who doesn't like a discussion like this...
For the term "bush is hairy" to be tautological and/or autological, it would depending on how the base terms "bush" and "hairy" are defined.
For the statement "her bush is hairy" to be "tautological", which means either (a) needless repetition of an idea, statement, or word; or (b) a statement that is true by virtue of its logical form alone, i.e. a logical combination of sentences that is always true (Merriam-Webster), the word "bush" would have to mean "hairy" to satisfy (a) or (b). Is there a circumstance where "bush" could be used to describe any amount of hair, and where the term "hairy" is used to describe only a large amount of hair. Consider how to describe a trimmed landing strip type of patch, there is some hair but is it "hairy". In such circumstances, the phrase "bush is hairy" may not qualify as being "tautological".
Regarding "autological", which is "of or relating to an adjective that is self-descriptive", i.e. an autological word is a word that describes itself (Oxford Reference), if the term "bush" were to include having "hair" regardless of the amount of hair, and where the term "hairy" is used to describe any amount of hair, then the statement "bush is hairy" would be "autological" as bush would include hair. However, if "hairy" is specifically defined as requiring a large amount of hair, and since there are situations where a bush does not always have a large amount of hair (trimmed landing strip), it could be concluded that a bush may have hair but is not hairy. Under those circumstances, the phrase "bush is hairy" would not be autological.
So, depending on the definitions of "bush" and "hairy", the statement "bush is hairy" could be autological and/or tautological.
After this exercise of the logic of the english language, I need some bourbon! Happy Hobbying!