Did you try just (kbd "s-s")? Does that not work? (I don't have a Super key, so I can't check.)
There should be no problem with the two s occurrences meaning different things. As a modifier, s- is realized by the Super key.
But it's a good question, considering that you can also define plain s as a prefix key, in which case, for example, you could have the key sequence s s, which would be the prefix key s followed by s (same key). That's different from s-s, however.
UPDATE
The Emacs manual Glossary says this about a Super key:
Super is the name of a modifier bit that a keyboard input character may have. To make a character Super, type it while holding down the <SUPER> key. Such characters are given names that start with Super- (usually written s- for short). See Modifier Keys.
So maybe try (kbd "Super-s"). Or even (I doubt it) (kbd "<SUPER>-s").
And the Elisp manual, node Other Char Bits says:
The X Window System defines three other modifier bits that can be set
in a character: “hyper”, “super” and “alt”. The syntaxes for these bits
are \H-, \s- and \A-. (Case is significant in these prefixes.)
Thus, ?\H-\M-\A-x represents Alt-Hyper-Meta-x. (Note that \s with
no following - represents the space character.) Numerically, the bit
values are 222 for alt, 223 for super and 2**24 for hyper.
So maybe try [?\s-s]? E.g. (global-set-key [?\s-s] 'forward-word)