bluetooth draining my phone faster

Bluetooth was specifically designed to be very low power. With a bluetooth headphone there is a battery in the headphone to power the amplifier and provide the energy to move the speaker diaphragm. With passive (wired) headphones, this has to be powered by your phone.

Do you really think that a phone that has to directly drive the speakers in a headphone uses less power than a phone that only has to power the bluetooth transmitter?

I love wired headphones, but I wouldn’t ever drive them directly from my phone. Especially higher end headphones are more difficult to drive anyway, so I use a (wired) external DAC/amp with it’s own internal battery for using my wired headphones.