Bluetooth Headphones and Nike Watch

Nike Apple Watch?

Do you have to have phone along to listen to music with Bluetooth headphone? I would like to leave the house wearing only Nike Apple Watch and Bluetooth headphones...is this possible? I currently have Apple Sport Watch (original) and try to connect BT headphones it connects with phone in range, but I can get it to connect with BT headphones and the watch only, hence I have to take all three with me- phone, BT headphones and Sport watch... What am I doing wrong?