There are two main ways that you can handle output from a media player like Media Center:
1. You can send the audio to the system audio mixer, which will generally accept anything you throw at it, and let it figure out what formats are supported by the connected hardware and resample to whatever it deems best.
2. You can have the player bypass the system audio mixer (also known as "bit-perfect" output) and take control over the playback device directly.
In scenario #1, the system might see that the hardware is capable of up to 96kHz and decide that it will resample everything to that, no matter what the input is.
In scenario #2, the player will take control over the hardware so that when you send it a 44.1kHz file, the hardware is outputting 44.1kHz rather than resampling it.
The issue is that most hardware does not accept all input formats, so if you were to send 96kHz hardware a 192kHz file, playback will fail with an error in scenario #2.
This is why Media Center offers controls to let you resample any input rate to whatever output rates suit you.
Some hardware might accept up to 96kHz but lack support for 88.2kHz for example, so you might want to resample that to 44.1kHz rather than 96kHz.
In your case, the best solution would probably be to set up separate zones for your MacBook's internal speakers, and another zone for your Bluetooth speaker, with separate output formats selected for each.