As far as I understand - if you want to use a bluetooth headset you need to have the Roku app on your phone use the phone as a remote and there is an option to use a headset on / with the phone. If you want to send media to the tv from your phone then you would want to mirror your phone.
I figured it out, but the remote is almost useless. keeps disconnecting and then saying the tv is in eco mode and it has to power it on (while the tv is on and playing netflix), and then there's the spinning circle and nothing happens. This has to be the least smart of any smart devices I own. Really disappointing for something so incredibly basic.
How well it works is up to your wifi connection. Mine works reasonably well with a TCL TV but I had to move the wifi channels to ones with the least conflict with neighbors and found that it worked best with the TV on a 5Ghz channel and my phone on a 2.4Ghz. That might not be necessary if you had one of the newer routers that can communicate with multiple devices at once (mu-mimo).
I bought a bluetooth transmitter. Avantree. Use the optical cable, in optical mode and there's no lag. You can go cheaper but consider line of site when you buy the device. It works perfectly for wireless headphones. Well, almost. Sometimes I have to reposition the antenna. There is a simple one touch button for reconnecting from the transmitter box. I already had it for my 10 year old Sony which predated wide spread use of blue tooth.
Add a bluetooth transmitter to the audio out port of your Roku TV, and then attach to the bluetooth transmitter. That's how I attach wireless devices to it. Adding a bluetooth dongle to the USB port might work, too.