In 1 Peter 2:9 -10 it says "But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light: [10] Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy." If you read chapter one, verse one it clarifies that the audience is Galatian, Asian etc so I believe that although the people Peter is speaking to might comprise Hebrews it is not very likely they ALL would have been so even though Peter is traditionally known as the Apostle to the Jews referred to in the Bible as "the circumcision" (Galatians 2:7-8). So technically I would say yes, the Bible is a book about a race, it is about the race of mankind, about our frailty and inability to walk in obedience to HIM and it is about GOD'S grand plan to rescue this race. There is something I would like you to consider with regards to your statement about race as I perceive you to mean it; even before CHRIST came any tribe etc could choose to follow the GOD of the Israelites (I believe these were referred to as proselytes) as evidenced in Acts 8 from verse 26, the man Philip spoke to was an Ethiopian who came to Jerusalem to worship. Ethiopia is a country located in the eastern corner of Africa it is unlikely that he was anything other than Black. This tells me that GOD'S people are those who HE has chosen and who choose HIM and this is illustrated often in the Bible. In closing, "Revelation 7:9 KJV After this I beheld, and, lo, a great multitude, which no man could number, of all nations, and kindreds, and people, and tongues, stood before the throne, and before the Lamb, clothed with white robes, and palms in their hands;
Revelation 7:13-14 KJV
And one of the elders answered, saying unto me, What are these which are arrayed in white robes? and whence came they?And cried with a loud voice, saying, Salvation to our God which sitteth upon the throne, and unto the Lamb. And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb.