Is bluetooth hardware or software

Bluetooth is neither hardware nor software. Bluetooth is a protocol definition for short-range wireless communications for (relatively) low-speed Bluetooth devices. It is not intended for general-purpose networking or security.

Bluetooth is formally documented by the Institute of Electrical and Electronics Engineers as IEEE 802.15.1.

Bluetooth is implemented as a hardware interface in computers, phones, tablets and other programmable devices using device driver software to communicate with Bluetooth devices.

Bluetooth device include hardware such as keyboards, mice, game controllers, headphones, speakers, mobile phones, etc..