Hi Jess,
I'm assuming you're using ArcMap.
In the Add Raster to Mosaic Dataset tool - I think you need to change your Input Data type to "Dataset" to find rasters within the .gdb. Once you've selected a raster it should be listed in the Source list
If you're still having issues adding a raster:
Go to the Geoprocessing menu -> Geoprocessing Options
Uncheck "Enable" in the Background Processing section. Ensure that "Stay up if Error occurs" is checked.
This will allow you to gather a conclusive error code on why the process is failing. If it's not a obvious error code, please post it back here to see if we can help you!
A