Galaxy Exhibit 4G Android 4.1 firmware

Android 4.2.2 is already available for the Samsung Galaxy Exhibit 4G but as you already know, Bluetooth does not work in it. Fortunately, there is another jelly bean ROM (Android 4.1.1) in which Bluetooth works as well.

Galaxy Exhibit 4G Android 4.1 firmware

The developer says everything works in it.
GSM (Both calls and data)
Audio
Wi-Fi
GPS
Compass
Bluetooth file transfer
USB mass storage
HW acceleration
Google Now
Camera
Tethering

You can download the firmware from here. You must perform the full wipe before using this ROM.