If you're trying to culture from a bottle, I'd encourage you to leave a bit of the beer behind as well. Any cells that are still in suspension are likely to be much more viable than the ones that have already dropped out.
You also want to use a lower-strength starter for your first step to put less stress on the yeast. I've strted using 2oz of normal-strength starter to 2oz of beer, which will dilute to a half-strength starter. The beer also acts as a bit of protection for the yeast, as the lower pH and alcohol content will inhibit some potential contaminants.
I pour the beer into the starter in a mason jar, then shake it until it's pretty much all foam to oxygenate it well. I usually let it go for 5-7 days before stepping it up to a normal-sized starter.