Some time ago (before Bluetooth Low Energy support for devices was much improved), I wrote a guide to enabling logging to see which BTLE devices HASS can see:
Things have moved on with improved drivers, and much better device support so this method would only confirm the BTLE (not the same as BT) address and manufacturer_data of your hardware which might be useful to check if someone’s code might work.
Sadly, I’ve not heard of a BT bed, and can’t help explaining what is likely to be a quite technical task.
Start small, and check out the Home Assistant Community Store first.