Where does the Bible indicate that it should be its own interpreter?
It doesnt specifically say that, but there is away to prove that it can interpret itself. I'll show you a simple example.
What might you think if you read this verse on its own:
Hebrews 12:13 keep making straight paths for your feet...
This could be interpreted to mean that we make our own paths straight. That the power is in our own hands to do so. Predestinarians actually use this verse to claim that we are 'predestined'
However, now read this verse at Prov3:6
In all your ways take notice of him and he will make your paths straight
This verse seems to say that God makes our paths straight. So which is it? Do we make our own paths straight or does God make out paths straight?
Well if we take into consideration that Jeremiah 10:23 says
It is not in man that walketh to direct his own steps.
this seems to tell us that we cannot direct our own step...its 'not in us' so obviously the first verse is not telling us that we can do that on our own... we need help.
So what help do we need to make straight paths for our feet then?
Psalm 119:9
"How will a young man cleanse his path?
By keeping on guard according to your word"
The bible has interpreted itself and told us that we make straight paths by following Gods word. So we can take the words at Hebrews to mean that we must individually 'apply Gods word' in order to make our path straight. It has nothing to do with predestination and the power is not in our hands alone. The path we choose, if based on God word will make our paths straight.