As a bit of background, I had a vaguely similar problem with wanting to get my Logitec programeable remote to control my gen. 2 VTV box.
I decided that as the VTV remote was bluetooth, my IR Logitec would not learn to control the VTV box.
But the instructions that come with the remote says that it can learn to control some functions of most TV's.
To find out how this Biuetooth remote can control an IR responding TV, I held a digital camera in front of the remote and pressed the power button. Well lo and behold, when the button released, the remote fired off a flash of IR commands and controlled my TV.
So the remote can send out simultaneous Bluetooth and IR commands.
Whether or not the VTV box responds to IR commands will decide if you will be able to get your Bose remote [which I assume is IR] to operate it.