It varies between Old Testament (OT) & New Testament (NT). Here's the latest numbers

Handwritten NT Manuscripts (by language)

 5,900 Greek

10,100 Latin

 2,000 Armenian

 4,000 Slavic

 2,000 Additional languages

24,000 NT Manuscripts

Handwritten OT Manuscripts

42,300 OT Scrolls (majority are in synagogues)

For comparison the average number of copies we have of the top 10 most frequently found books/scrolls from ancient times is only 15 copies! The Bible is the by far the number one book of antiquity with regards to it's number of copies. Second place is Homer's Iliad which only has 1,900 total. That's only 4% of the copies we have for the Bible. If you were to stack the copies of OT and NT they are over 2 1/2 miles high and the average book of antiquity is only 4 feet.

Additional Sources

• Evidence that Demands a Verdict by Josh and Sean McDowell
• www.danielbwallace.com