Using Bluetooth module HC-05 when Arduino is powered using a battery
6F22 (PP3) batteries are among the wimpiest of batteries available.  They are not a good choice for anything except extreme low power applications, and anything involving radio transmitters is definitely not an extreme low power application.

Use a better battery.  I would recommend 6 AA batteries (you can get 6xAA battery holders with the same connector as a PP3 battery) which will give you considerably more power than a little PP3.

Either that or a 7.2V "2S" Li-Ion battery pack.