Shipping a bushy 3gal plant is likely to cost far more than the plant itself. I would think you can find one in a ~4in pot for a reasonable price.
edit - not as bad as I thought. $25 to ship UPS ground a theoretical "7lb 3'x1'x1' package to Chattanooga"
btw you probably want two pitangatubas for pollination as they don't set fruit well on their own. They fruit really early from seed, if you find two small seedlings you can probably have flowers within a year or two.