Bubble Tea has been around Louisville for a while, but you've had to look for it. Coco's Bakery, as noted, has it, and so did its predecessor in the same location. TaiPei in the Fourth Street Live food court has it in season. I wrote a piece about it for LEO a couple of years ago.
That said, it has been a minor presence, more of a little "cult" secret for a few admirers than anything resembling a trend. I think it's cool, and I'm still charmed by a friend's description of her then 2-year-old granddaughter discovering the tapioca bubbles at an eatery in Memphis, where it's a little more widely available than here.
Here's my bubble tea piece (about TaiPei) from July 5, 2006. Page down past the beer brown cow to find it.
http://www.louisvillehotbytes.com/?p=76