Not possible. Bluetooth in iOS does not support file transfer.
Bluetooth is supported for stereo headsets/speakers, handsfree
telephone devices/headsets, some keyboards, some peer-to-peer
apps from the app store and internet tethering where provided
by the carrier. Other than this it will not connect to a
phone/computer/device. (thanks to ckuan for the wording)
It would have to be a feature that Apple would have to add to iOS. Whether they will ever do so is something none of us here will know. You can express your interest in such a feature to Apple via their feedback page: