Mushaf was used by classical writers in their manuscripts in reference to a bound book. For example the author Jaahidh referred to each section of his book Al-Haywaan as a Mushaf and
at the end of each section he would write, “thus ends the first Mushaf and begins the second Mushaf. . .”
Also, Sheikh Aba Bakr bin 'Iqaal Saqli in Fawaa'id says, “The sahabah didn't collect the sunnah of the Prophet of Allah(s.a.w) in a book (Mushaf).” 1
It's worth pointing out that the word Mushaf is mentioned neither in the Quran itself nor was it counted among the names of the Quran. Jalaaluddin Suyuti2 and Abu Al-Ma'aali al-Saaleh, who was one of the transmitters of hadith of Islam, counted 55 titles for the Quran and the word “Mushaf” was not among them.
It's interesting to know that no one objected to Seebway's calling his book Al-Keetaab, despite the fact that that was one of the titles of the Quran, but they object to the book of Lady Fatimah(a.s) being called “Mushaf”.
Dr. Imtiyaaz Ahmad in his book Dalaa'il al-towtheeq al-mobakkir lil sunnah wa al-hadeeth says that Mushaf doesn't just refer to the Quran, but can refer to (any) book. In order to prove his claim, he cites several sources.3 Also professor Bakir Bin 'Abdullah in his book Ma'rifat al-nasakh wa al-sahhaf al-Hadeeth says, ”'Mushaf' is an idiomatic expression which is inclusive to any collected work used by speakers.”4
Dr. Nasiraddin Asad in Masaadir al-shu'ur al-jaahili writes, “They called any bound book a “Mushaf” and it strictly refers to a book, not just the Quran.”5