Do you have any friends or relatives traveling back to Israel from the US or someplace that does sell bottled Kombucha? Starting with proper mix of bugs/yeast is always easiest. Next easiest would be to try to a sour ale yeast/bug blend like I pointed out above. A decently stocked homebrew store should be able to get some...
Failing all of that, you can do the "from scratch" thing. It may take a couple of months, as in that other thread I pointed to, and the results will be unpredictable, but it might work. I've never done it. There might be better instructions for starting a wild SCOBY online (google is your friend) but here's how I might go about it:
Make a gallon or so of black tea and cool to room temp, add some sugar and cover loosely with a dish towel. This should keep out dust but let wild bacteria and yeast in. Maybe stir it everyday and smell/taste to see if it's changing. Ideally you'll want the wild yeast and bacteria to take over before any mold starts to grow. Let it go a week or 2. Drain off the spent tea except for a cup or two and add new tea and sugar. You may need to do this 2 or three times. You'll hopefully end up with a gelatinous mass that floats on the surface, that's your SCOBY.
You might be able to speed it up by putting a freshly picked and unwashed piece of fruit in the tea. Like a plum or apple or grapes... There are wild yeast on the fruit. Heck, even a pinch of bread yeast or brewing yeast might work. Maybe spoonful of sour dough bread starter or live culture yogurt for some lactobacillus, or even raw wheat. Perhaps a table spoon of unfiltered apple cider vinegar for the acetobacter.
Actually, now that I think about it, your ginger bug might work, too. Brew up some strong black tea, add sugar, cool it and add your some of your ginger bug.
It may take some experimenting to get the right combination of Sacc, Lacto, Aceto, etc. Especially from wild sources.
Keep notes, and then come back here and tell us how it worked!
http://en.wikipedia.org/wiki/SCOBY