I'm a little hesitant to put much stock in conservatives' claims of bias, because plain factual reporting tends to strike a lot of them as biased. Reality is biased against modern conservatism.
I don't think the BBC is the worst by any means. But a couple of years ago, they did come out with one of the most egregiously misleading articles I've ever seen with regards to transgender people. Very obviously deliberate in its misinformation and even including proven lies about contacting sources. And to this day the BBC stands by it and has dismissed complaints.