No one ever said that someone gets saved because they read the Bible. It's always through Jesus by faith. But it's through the Bible that we even know about Jesus and what He did. Faith comes by hearing and hearing by the word of God.
So sometimes someone reads the Bible and learns about Jesus and accepts Christ that way. Sometimes it's by hearing someone else tell us about Jesus and what He did.
Either way, salvation is through accepting Christ, regardless of the mechanism by which the message is heard.
Amen. That Romans 10 reference is powerful.