I am late to the party, but dkfick gave you excellent advice. I have cultured and plated yeast from many bottle-conditioned beers. The number one mistake that most amateur brewers make when culturing yeast is attempting to make a starter directly from bottle sediment. That technique only works when using the sediment from a bottle of really fresh normal gravity beer. I usually start 40mls of 5% w/v (1.020) autoclaved wort using the last 10 to 15 milliliters of liquid from a bottle of bottle-conditioned beer (it is difficult to swirl the sediment into suspension using less than 10mls of beer).
Another common mistake that amateur brewers make when culturing yeast from a bottle is forgetting to flame sterilize the lip of the bottle before decanting the beer and the yeast (I usually swab the lip with 90% alcohol before flaming it). This step reduces the chance that wild microflora will be picked up during the transfer. The number of viable cells in a bottle of bottle-conditioned beer is often very low; therefore, one wants to make it difficult for wild microflora to hitch a ride during the transfer. If I am working with an older bottle of bottle-conditioned beer, I will usually perform the transfer over a flame source. When flame sterilizing the lip of a bottle, one only needs to make a few passes through the flame source. There is no need to heat the glass until it is hot, as doing so will often result in fracturing.
Forty milliliters is a small enough volume of wort that one should see active fermentation within 48 hours. A bottle that has viable domesticated yeast cells should produce active fermentation within 48 hours. One can assume that any S. cerevisiae or S. pastorianus culture that fails to start in 40mls of 5% w/v wort within this period of time is non-viable. One can safely assume that any S. cerevisiae or S. pastorianus culture that starts after 72 hours when pitched into 40mls of 5% w/v wort is infected. This rule of thumb does not always hold, but it holds often enough that one should be hesitant to propagate a culture that failed start in 40mls of 5% w/v wort until 72+ hours after pitching without going through single-cell isolation and testing.