For some reason it would appear that by default, your IIS is not allowing access to your bin folder. This is probably inherited from the parent site above your virtual directory. Regardless, see this link regarding FileIO with medium trust:
http://msdn.microsoft.com/en-us/library/ms998341
You likely need to add a section to your web.config to provide specific access to your AppDir to override the setting from the parent site/virtual directory.
<IPermission
class="FileIOPermission"
version="1"
Read="$AppDir$"
Write="$AppDir$"
Append="$AppDir$"
PathDiscovery="$AppDir$"
/>