Hi MattEMatt ,
The "Bring Your Own Meeting", or joining the meeting on your personal device but automatically pulling in a room system works in 2 ways: by proximity (i.e. the phone/laptop 'hears' the nearby MTR and offers it automatically as a host for the meeting) or by the "Suggested Rooms" list which is a list of rooms that you've used recently or frequently on your calendar from the Exchange/O365 Graph. These are mutually exclusive. Proximity is not in any way informed by the Suggested Rooms list, and Suggested Rooms does not in any way rely on location or proximity.
The only way you'll ever see the banner show up on pre-join is in the case of proximity, when you are very close to a room system, it will be offered as a choice to join from in pre-join.
If you do not see that banner, or if you want to join from a different room, you can choose "Add a Room" from pre-join. Doing so will take you a screen that shows your Suggested Rooms from the calendar service, combined with all rooms that are nearby using proximity, in the same list. You can also search for a room if you don't see the one you need there. You can tell in that list if a room is nearby (your device hears the bluetooth beacon) or if it's a Suggested Room, by the icon that appears to the left of the room name. If it's the location beacon icon, it means it's nearby. We de-dupe that list and show them using nearby rooms first.
As for the features called "Location Based Services", this is basically a permissions & privacy setting on mobile phone OSs that require Location to be enabled for the Teams app to listen for BLE beacons. It's a means to provide privacy control to users.
To help diagnose your situation: on the laptop, if you go to the second page from the "Add a Room" link in pre-join, do you see any rooms at all with the location beacon icon? If not, the laptop may have bluetooth turned off, or may be hitting a known issue where the Windows installation on that machine is 64-bit, but the Teams app installed is the 32-bit version. There is a documented gap in Windows where they do not report radios to 32-bit apps from 64-bit OS versions. If that's the case, please install 64-bit Teams and you should be fine.
Hope that helps,
greg