In essence, the ginger "bug" is a wild yeast, and you can just pour some of that yeast starter you already have going into a new jar with other fruits and it will start eating their sugars.
And yes, you can use the same method to get wild yeast from blueberries, currants, blackberries, pineapple, and the easiest one of all is from ordinary raisins. You can use the yeast from any of them to make almost any kind fruit juice fizzy and somewhat alcoholic. One of my favorites is to make a fizzy alcoholic orange juice.
In essence, you're making a fresh fruit (or root) wine.