According to this article on the BBC web site, an open invitation to submit evidence of bias against climate change doubters' research revealed almost nothing.
The opposite case is also interesting to contemplate – that there's a natural bias in favour of contrarians, even if they have nothing to offer.
If climate scientists are successful in making the case that the problem is really, really serious, the obvious next step is not more funding for climate science, it's more funding for alternative energy. By making the case as strongly as possible, rather than making it easier for them to earn grants, they are making the case that funding should shift to an area in which they have no competence.
On the other hand, who does benefit from stringing the debate out? The deniers, especially those whose work isn't very good. A fair number of papers and even books have been published because of the mindset of being "fair", allowing a contrary position space, and so on – which shouldn't have been published on their merits ... Soon's work on solar effects using bogus data, Lomborg's ("I taught a class in statistics for social scientists so I'm a statistician") books misusing references on a grand scale, for example).
And of course there is a fair element of being in denial on the possibility that the science is right, hence the backing by normally careful editors of the Economist and Wall Street Journal of contrarian positions with little or no substance.
Bias? I would say it is on the side of denial, not on the side of the mainstream.