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Short answer: you’re passing Store as a value. All your menu functions should take a Store& or Store* instead.
When you’re passing Store as a value then an implicit copy is done (so the mainStore variable is never actually modified). When you return from the function the Store::~Store is called to clean up the copied data. This frees mainStore.bookList without changing the actual pointer value.
Further menu manipulation will corrupt memory and do many double frees.
HINT: If you’re on linux you can run your program under valgrind and it will point out most simple memory errors.
Your Store contains dynamically-allocated data, but does not have an assignment operator. You have violated the Rule of Three.