Honestly if the height is 4.5mm then it mean the width of the bridge section is what, 10mm wide? If you print cold and slow I think you would not even need supports except for the round perimeter. As mentioned above, look at the posted link.
http://support.3dverkstan.se/article/38-designing-for-3d-printing#custom-supports
0.01mm is too small of a distance. It will connect with the border. 0.4mm wide lines are too thin. Even if the print head is 0.4mm wide it need to be able to pass twice (assuming you are using Cura) on those sections unfortunately so try with 0.45mm.
You can easily see what the results will be in Cura. Load the object, let it slice, go in layer view and validate your tests.