re:
I got this issue and finally could solve it with the simple way. I reset my Windows Phone after updating it to 7.8 version, but nothing I could do for Bluetooth Share. I don't know if this work for you, but I found myself happy because I could find Bluetooth Share on my Marketplace.
I am from Indonesia, so I use my operator career in my country. You may do some following procedures:
1. Please 'Reset' your phone. Make sure you have backup the data.
2. After Resetting your phone, make sure you don't enter your Windows Live ID with the existing account that you have previously.
3. Please select 'Create New Windows Live ID' right away from the prompted message on the screen. Create the new one and you have to FORGET the existing one.
4. Please wait until your WP is finished installing the needed application according to your location.
5. Open Marketplace and type 'Bluetooth Share'.
6. You must find that application on the search result of your WP Marketplace.
7. Install it and have fun with your Bluetooth capability for transferring and receiving photos and musics.
Note:
It worked perfectly with my region Indonesia. I found the news that it could be available in the certain Region. You may check the link Bluetooth Share | Windows Phone Apps+Games Store (United States)