Probably your NetworkManager is setting the wifi device to sleep - power save, and the Bluetooth device is embedded inside your wifi card.
You can try to disable Radio power save editing this file :
/etc/NetworkManager/conf.d/default-wifi-powersave-on.conf
[connection]
wifi.powersave = 2
As described here the wifi.powersave can take 4 values :
From the source code: wifi.powersave can have the following value:
NM_SETTING_WIRELESS_POWERSAVE_DEFAULT (0): use the default value
NM_SETTING_WIRELESS_POWERSAVE_IGNORE (1): don't touch existing setting
NM_SETTING_WIRELESS_POWERSAVE_DISABLE (2): disable powersave
NM_SETTING_WIRELESS_POWERSAVE_ENABLE (3): enable powersave
Please try it out. Good luck 