I recently had to take a quick trip to Bangladesh. While searching the United site, I found some good space on Thai, EVA, United and Asiana. All the airlines have flat bed seats, but I leaned toward EVA Air because they joined the Star Alliance two months ago, so I hadn't yet had a chance to fly them.

EVA flies the same flat bed business class seats as Cathay Pacific and the new American Air 777-300ER, which are widely considered the best business class seats in the world.