Airplane mode generally disables all wireless connections, including Bluetooth.
EDIT: researching it that could be just a "be safe" catch all though, and regulation might actually mean just cellular in some cases. No idea how a normal person is supposed to figure out what exactly applies to the current flight then.
I worked at an airline two years ago on the rollout of inflight wifi and they advise customers to enable airplane mode and reenable wifi (if it's disabled). These days within aviation, "airplane mode" refers to disabling just of the cellular radios.
