Hmmm, I realized I skipped over couple things here. For ginger beer what I do is start with a small ginger bug. This one I might keep going for a while. When this is active, I step it up to a larger volume with roughly the same proportion of sugar/water/ginger. When this big bug is active it goes in my beer. This one usually takes off faster than the original bug did.
This stepping-up process is really the same principle as making a yeast starter for beer or wine. It simply ensures you have plenty of bugs to get things rolling.