Melanie, you can use your water kefir/tibicos ferment as a secondary fermentation, as you noted. You can make a ginger bug, if you don't mind having a little ginger flavor. You can step your ginger bug up (once active) with just sugar water to dilute the ginger flavor.
You can also use brewer's yeast or even common bread yeast. Using yeast is essentially making a "small beer," meaning it's fermented like beer, but has very low alcohol (practically non-alcoholic).
You can also just leave some of your pre-fermented soda sitting out, stirring it often (cover with cheesecloth between stirrings) and wait for it to start spontaneously fermenting. Then bottle it when you see bubbles starting. This too will be mostly yeasts working, but will also have some Lactobacillus in the mix.