The surfaces for writing on in the ancient Mediterranean and Near East were papyrus, clay (where papyrus was unavailable), wax on wood (for short-term notes), and parchment. Paper didn't arrive in the Mediterranean until the 8th century CE, at which point the idea was imported from China. European paper at that time was made of linen or hemp rather than wood.

Put another way, paper was invented once (in Han China) and from that one-time invention it eventually spread over the world.

I don't have access to Bauer's book, but it would be easier to assess the exact nature of the claim if you could tell us her exact wording and context when she makes this implication, and/or what evidence she cites. If, for example, she claims only that the Egyptians invented the first paper-like writing material, that would be more defensible.

Was it the Egyptians who invented papyrus? Or the much later Chinese?

The Egyptians invented papyrus; the Chinese invented paper. Papyrus is similar to paper - so similar that it is the root of the word "paper," but papyrus is made using different materials and methods than paper (to be fair, their are different sorts of paper, but papyrus is generally considered a separate material).