Can I use Bluetooth to hear TV in a second room WITHOUT losing the sound in the TV room?

Not directly with the Roku.  You'd have to find some external product that can do what you want such as a splitter to send the audio to some bluetooth device.

If I'm understanding what you're asking, the firmware itself won't allow this without an external device (AVR, etc).

When the audio is redirected (via remote and/or Roku App on the phone), I believe it automatically disables audio on the TV.  There used to be a key sequence you could use to enable both, but I don't think it's supported anymore on any device.  I don't remember the sequence off-hand, but you can search for it on the forums if you want to try.

try to follow me on this:

if you have a dedicated FIXED ANALOG AUDIO OUT on your tv(it would either be a 3.5mm connection, or a red and white rca out) then you can buy a blue tooth adapter on Amazon that allows you to either send or receive blue tooth  signals:

here is a link:

https://www.amazon.com/gp/product/B01B4 ... UTF8&psc=1

This little unit works well, but does take getting used to how to use.  If you use it the way I describe, you can connect it to any tv, use blue tooth headphones, and the speakers still work on the tv.  You would also be able to hear sound from any source(input) on the tv.

HDTV's with BLUE TOOTH built in, TURN OFF the external speakers when using the internal blue tooth function.  This little unit does not do that.  It has the ability to either SEND or RECEIVE Blue Tooth, so it has multiple uses.