I'm trying to export one of my meshes however the options which I normally would have when exporting my mesh as an FBX are missing. Primarily what I need is to export selected objects only as it's exporting the entire scene.
I am guessing you have a bad UI layout in file.
(They changed the export layout in 2.81. Did you open up the 2.81 beta, save the file, and return to 2.80?)
Try to close blender, Re-open it with default scene, go to File->Open, deselect "Load UI" and open your blender file. Export settings should be back now.
If that does not work, (Or you are also missing the Open Blender File settings), go to File->Defaults->Load Factory Settings, then File->Defaults->Save Factory Settings.
Restart blender and try to deselect "Load UI" again.