HI, i have musicbee on my laptop which is then connected by HDMI cable to my Sony Bravia works great!
The OP wants to install MB on an external drive and connect that to the TV. Once the portable drive is disconnected from the PC there is no OS, so it's not very likely MB can run directly from the TV.
While the portable version of MB is indeed portable, it still needs an operating system in order to work. If the OP's TV is a Windows TV, then it might possible work. But I don't think such a thing exists. Feel free to search the Internet.