Because the BBC is tax-payer funded, it always has to hide its Left-Liberal - sometimes outright Leftist - bias. After all, everybody pays for the license fee - no matter what their political beliefs.
So there is rarely any outright politicking on the BBC (except on Have I Got News For You, other BBC comedy programmes, dramas/soaps, opinion pieces, etc.).
The BBC shows it bias by what it focusses on; what it misses out; who it quotes; who it doesn't quote; what it quotes; etc.; rather than by plain politicking.
I don't think that every BBC presenter and BBC programme is Leftist or Left-Liberal either. That doesn't matter. It's the BBC's editorial line and overall bias that's Left-Liberal. Every now and again, then, they will have shows presented by right-wingers, etc.; which is more than The Guardian ever manages. (The Telegraph, on the other hand, does publish pieces by what could be called Left-Liberals.)
Of course it's a little embarrassing accusing the BBC of bias because all kinds of mutually-contradictory political groups do the same. However, all I can do is argue my case. And it must also be borne in mind that many BBC presenters, editors, programme makers, etc. have explicitly admitted to that (left-liberal) bias at certain times. (Quite a few times, actually.) Others have also denied it.
Take the case of those Leftists who say the BBC is based towards Israel. Succinctly, that amounts to saying that the BBC doesn't completely endorse and propagate the revolutionary Marxist analysis of Israel (that it's an “imperialist racist state”) in which Israel has literally sole culpability for.... um, everything that happens in that area of the world. Well, if that's what the BBC must believe in order not to be biased, then the Trotskyists/communists are correct: the BBC is biased.
In addition, when I say that the BBC is biased I don't also believe that such a news outlet can necessarily escape from such bias: it can't. What it can do is admit to its bias (as it has done at times) and also try to allow outlets for other perspectives; which, to some extent at least, the BBC has done.