Bias and fake news are two separate things. Every news source will be biased and it is impossible to separate the bias from the reporters, editors, or any humans involved in presenting the news. Bias is favoring one side over another, leaving out facts that hurt your case etc.
Fake News is an entirely different thing. Fake News is making up real-looking websites that claim Elon Musk is running as a Libertarian candidate for 2020.
BBC has had a few incidents lately which screamed 'fake news!' to me too. So I totally get where you're coming from. But conflating bias with fake news has hurt trust in the media more than the actual fake news itself. And that's the actual reason for spreading fake news. Because I'm fairly certain you wouldn't believe in outright conspiracy theories. But if you start to treat actual news sources like AP or Reuters just like fake random-city-ledger.com websites, then the fake news sites are succeeding.
Personally, I look for motivations regardless of the source of media - who benefits from this story if it was true vs. false? Is Bernie really going to charge 95% tax to everyone making 100k or above? If it's remotely true, then obviously it would hurt everyone who works hard. However, if that story is false, which it most likely is, who does that benefit?