Make your selection by whatever means you chose, then go Select>Save Selection.
A dialogue box will appear asking you to name the selection, which PS will save as an Alpha Channel.
Hope this helps!
The only problem is, it doesn't give me the option to save the selection, only 'Load Selection'
Make sure you are on a pixel-based layer, or layer pixel-based component inside the Layers Panel and then check your selection pull-down menu again. If you have a pixel-based layer with a mask component and you have the mask selected as the active component you won't see the Save Selection option.
From your screen Capture it looks like you did save the selection as Alpha 1
That your in quick selection mode because if the red overlay
In Quick Selection save selection will not be an option
You can save the selection by dragging the selection in the channels palette to the new channel Icon
You can also load the selection using the load selection icon in the channels palette then use Save Selection
You can leave quick selection mode so you see the marching ants and then use save selection