Well if you want wireless you have two or 3 options Blue Tooth and Wi-Fi. are the wireless ones. #3 is Wired.
Now... If you are good with Linux a Raspberry PI might work Some of them support either BT or a BT dongle (2 3 4 all support dongles as I recall) There are some other options too.
I just spent (by the time it's fully set up about 200 dollars but 150) on a Vio or vivostick Windows 10 "machine" this puppy plugs into the HDMI port on the TV and eats USB power it's a full featured windows 10 running on an Intel Atom. about 3/4 inch by 1/2 inch by 5 inches 32 meg SSD. Tomorrow I'm putting it in full service but it set up and loaded the programs I want.
IT supports both Blue Tooth and Wi-Fi
Not sure how well you can stream to it though.
But if you want to do it wireless you have limited options
I used to know a man who made a micro tv station (Composit in UHF out analog) but well.. That was a long long time ago and I'm not sure they were type accepted.
