Dice rolls as entropy source?
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  What is the best method to make the bias go away?
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No matter if we’re talking about the bias coming from manufacturing flaws, or the bias we know from casino-quality dice, you can use the Von Neumann skew-correction algorithm to generate uniformly random data from skewed input.

The Von Neumann skew-correction algorithm was published in “Various techniques used in connection with random digits.” (NIST journal, Applied Math Series, 12:36-38, 1951). Since the paper is hard to find online due to its age and publication date, I‘ve put a copy in my Google Drive account (PDF) for reference purposes.

The general idea behind Von Neumann’s skew correction is to consider sequences of rolls/coin-tosses/whatever instead of isolate ones while picking a sequence length long enough that an even number of possible outcomes has equal probabilities. 

Explaining the Von Neumann skew-correction algorithm:

For dice, pick a sequence length where $n&gt;2$. The reason for picking a sequence length of $n&gt;2$ is that no subset of possible outcomes of equal probability for $n=1$ or $n=2$ has a cardinal divisible by $6$.

So, for this example, let’s simply take $n=3$. Doing so, the outcomes of any dice can be partitioned into 6 categories of equal probability according to the relative ordering of the successive numbers rolled – provided these numbers are all different. 

We need this, so that sequences can be grouped according to whether the second number is greater – 1 – or smaller – 0 – than the first, and whether the 3rd number is greater 111,011 or smaller 100,000 than both the first and the second, or between them 110,001. 

All 6 possible orderings will occur with equal probability because each of the sequences belonging to any of these orderings matches exactly one sequence of equal probability in every other ordering. Meaning: 1,2,4,1,2,4 matches the ordering 111, while 2,1,4,2,1,4 (which is equally likely to be rolled) matches 011.

EDIT

@fgrieu describes a different, yet equally practical implementation in his comment below.