Who has the authority to [discern] what the bible really teaches?
Wrong question. With that kind of thinking, you're setting yourself up to be deceived and manipulated by unscrupulous religious leaders who will always try to convince others that the Bible does not mean what it says but means what the religious leaders say it means. The correct question is...
Who has the responsibility to discern what the bible really teaches?
The answer? You the reader. See Mark 13:14 parentheses, Revelation 1:3 and 2 Timothy 3:15-17.
Think about this: If the Beroeans did not have the authority to discern what the bible really teaches, then what legitimate basis could they have had to compare Paul's teachings against the bible to judge whether or not he was teaching correctly? They would have been acting presumptuously. But the Bible said they were noble-minded.
If Christians do not have authority to discern for themselves what the bible says but must look to some hierarchical authority whose interpretations they are beholden to accept without question, then they are no longer trusting in God but in that human authority. They would be followers of the teachings of men instead of followers of what the Bible says. They would be making themselves vulnerable to being deceived and manipulated by those who twist the scriptures to serve their own interests.
Consider this too: how can any person know which church is teaching the truth and which is teaching error? Compare their teachings with the bible, you say? But how are you to do this if you don't have the authority to discern what the bible is really saying, in the first place? In other words if individuals don't have the authority to discern what the bible says then they don't have any means of testing any church's teachings in light of the scriptures since they have no authority to discern the scriptures. So you're proposing a situation where Christianity has to be based on faith in men's teachings and interpretations as being correct without having the authority to objectively determine if they're correct. Does that strike you as being a logically and ethically tenable position?
According to JWs, how did God make known to the first century Jews that he had chosen the apostles and formed a new Christian congregation as the approved way of worship? They say he empowered the apostles to perform miracles that served as indisputable proof of divine backing. Now look at the mess that exists today with 30,000+ conflicting denominations all professing to be true but teaching conflicting doctrines and using scripture to back them up. Is it reasonable to think that the God who provided 1st century Jews with miracle-working apostles, expects people today to wade through the mess on their own without him ever empowering his true earthly representatives to make themselves unmistakably known through some miracle? Is that reasonable. Search the scriptures and you'd see he always gave his representatives miraculous credentials to prove their divine appointment. Where's the miraculous credentials by the Watchtower or any other group? It's nowhere to be found.
There is obviously no God or none of the groups today are his special appointed channel.