Yes, you can bottle kombucha. You have to be a bit carefull, though. The problem is that when you bottle kombucha, there's still quite a bit of sugar left, and so you might get bottle bombs. Priming sugar is therefore usually not necessary. Of course you could let the kombucha ferment pretty dry before bottling, but then it will probably be way too sour! Note that hydrometer readings don't make much sense for kombucha, because there are different processes going on, with a different affect on the gravity readings.
If you condition the kombucha for a couple of days after bottling, you probably get nice carbonation. If you then store the stuff cold, you should be able to avoid over carbonation.
Personally, I let the kombucha set a bit longer, and then store in champagne bottles for extended periods of time, without adding priming sugar. This way I get a clear, well carbonated and well-aged kombucha...