Many integrations outside of officially supported ones (lamps, floor / desk fans, etc) are possible and some are documented in the forums (for example, Dyson remote
Most of the bed controls I know are 2.4 GHz RF control if wireless, and a couple others are WiFi enabled.
However, if an item is RF controlled within supported wavelengths (or IR and using a Bond Bridge [not Pro, as that model lacks IR]) and doesn’t have some abnormal encryption / modulation, you have a good chance of success.
285.5 - 505.5 MHz (Bond Bridge serials starting with ZZ)
300 - 450 MHz (Bond Bridge serials starting with A/B)