set the ClipURL to (the clipboard as string)

ignoring case
	if ((characters 1 through 4 of ClipURL as string) is not "http") then
		return "Malformed URL."
	else
		set curlCMD to ¬
			"curl --stderr /dev/null \"http://bit.ly/api?url=" & ClipURL & "&login=[replace_with_bitly_username]&apiKey=[replace_with_bitly_api_key]" & "\""
		
		-- Run the script and get the result:
		set tinyURL to (do shell script curlCMD)
		
		return tinyURL
	end if
end ignoring

You need to replace [replace_with_bitly_username] and [replace_with_bitly_api_key] to make this snippet work. Test in AppleScript code editor if you're experiencing problems in TextEpander such as the snipped being output instead of the bit.ly URL

TextExpander bit.ly

AppleScript