You can do it by reading the "Performing Long-Term Actions in the Background" part of this docs
Essentially, using state restoration, the system takes note of what your app was doing when it was killed.
If the app is searching for a bluetooth device and is killed by the system, the system will take care of continuing this research and wake up the app again when the bt device has ben found.
Note that this will work only if the app is killed by the system, not by the user (using the multitask bar). This behavior has changed since iOS 7.