Bluetooth sharing on the iPhone is one of the things Android and other platforms like to poke a stick at and make fun of. It's not exactly iPhone's forte nor the iOS ecosystem's good part. In fact, Bluetooth on iOS is sometimes a joke if you're thinking of file transfers.
But Cydia tweaks change the game altogether. For instance, the recently-updated AirBlue is a wonderful tweak that enables full-fledged Bluetooth sharing between an iPhone and all other devices including Android, Windows, Mac OS X, Linux and more.
AirBlue got updated to meet iOS 7-standards and to be compatible with the A7-devices: specifically, iPhone 5s. There's a dearth of such tweaks or apps that open the limitations of Bluetooth on iOS. And AirBlue takes the credit for being the most popular and the most functional tweak which does it. Almost perfectly.
With AirBlue installed, sharing files (of any type) over Bluetooth between any type of a device and your iPhone becomes pretty easy.
AirBlue lets you send files through the share option/share sheet available in most apps. That means almost every type of a file can be transferred. AirBlue supports native pairing which means you don't have to re-pair (not repair) any other iOS device that has been paired already with your iPhone.
AirBlue also supports Bluetooth sharing from other devices. For instance, you can send a file from Android smartphone or a Windows PC to your iPhone and AirBlue (on your iPhone) will take care of the share. New features have also been included with the update which make the tweak even more powerful. These include Wi-Fi support for faster transfers (between iOS devices only), Wi-Fi hotspot creation, importing contacts and photos to respective folders/parts of the iPhone etc.
AirBlue, for all its features, costs $4.99. It's on the BigBoss repo.