I don't think the sort of Bluetooth module you'll have in a phone will be fast enough to stream video. They're okay(ish) for audio as long as you don't mind the extra compression required to push music through the narrow bottleneck of a typical BT module, but video needs a whole load more data to pass through if you want to get more than a little low-res thumbnail video playing. That's why Miracast (Samsung/Android) and Chromecast use WiFi.
A typical BT module will max out at 1 Mbit per second. Even the latest v3.0 BT modules (which aren't in everything) don't go above 24 Mbit per sec. If you want to play videos then you're looking for a sustained through-put of 50 Mbit per sec or more. WiFi can achieve 50-150 Mbit per sec.
If you have WiFi at home then you might be better off investing on one of the dongles such as Chromecast or maybe a Firestick or an Android MX box and plugging that in to the TVs HDMI socket. These solutions are available from under £40.