I really doubt that many consciously ask whether something fits "the party line". They mostly introduce bias subconsciously in their decisions about what is and isn't "news".
Politician A accidentally says something stupid and it's ignored. Politician B accidentally says something stupid and it's "Politician B's Latest Gaffe" on the front page.
(Why yes, I do have a specific Politican B in mind, but shan't mention any names to avoid off-topic discussions.)
Anyway, it's odd that you would think that being a "non-corporate news provider" would insulate the BBC from bias. What about the natural groupthink which tends to accumulate in organizations insulated from real-world concerns?
I wonder when and where? I'm generally a big fan of the BBC but it's not completely above the fray.
Thinking back to times I've been living in the UK and the country has gone into war (most recently Iraq), the BBC reported on the political leadup reasonably even-handedly, but as soon as the shooting started Paxman took a break from Newsnight and instead we got Peter Snow running around a giant table with toy tanks on it (Americans: you switch on expecting PBS but get CNN instead).
Whereas I would, on the other hand, say the BBC was anti-war biased from day one. Which just goes to prove that "unbiased" journalism is impossible, since people only percieve bias when it disagrees with their own biases.
It's worth noting that even wikipedia doesn't attempt to be "unbiased" but makes the weaker claim to have a "neutral point of view". And it can only achieve that state via continuous edit wars between people holding all major points of view. And even then it's only an ideal, not a description of the state of wikipedia at any given time.
My recollection is that the BBC was not biased against previous wars - and I can recall the Falklands & the first Gulf War fairly well.
However, for the Second Gulf War they did keep asking "why are we going to war?" - which as it turns out was a perfectly valid question as the justifications for the war (and especially for UK involvement) ranged from rather weak arguments (Saddam is bad) through to outright lies (involvement with 9/11 or WMD).
So if the BBC is biased it seems to be biased in favour of the truth.
People perceive bias in the absence of bias. I remember in 2004 when Bush was re-elected, the local paper ran with the headline "Four More Years" and a smiling picture from Bush's victory party.
People wrote in and complained that it was a biased headline. They had imagined that the editor who wrote that wrote it with a heavy heart - even though Bush supporters themselves were chanting "four more years" to rally the troops at campaign events.