The control bindings are stored in an XML file (on PC). You can find it in C:\Users\<You>\AppData\Local\Frontier Developments\Elite Dangerous\Options\Bindings (or something like that). If you set up the controls, take a copy of the custom.binds file and rename it, then set up the next one and take another copy and rename that etc. You should then be able to switch your bindings by copying the one you want to use and naming it custom.binds.
Bit of a faff but there is no official way of doing it at the moment.
P.S. AppData is a hidden directory by default so you may need to set show hidden files. Like this for Win 7:
Select the Start button, then select Control Panel > Appearance and Personalization.
Select Folder Options, then select the View tab.
Under Advanced settings, select Show hidden files, folders, and drives, and then select OK.