there is no way to change this on auto-formatting in WebStorm 11; you can only use intentions here (hit Alt+Enter on quoted string, choose 'Replace double-quoted string with single-quoted string'.
Note that in WebStorm 12 -2016.x it's possible to control the auto-generated quotes style (used for auto-imports, etc.) - Settings | Editor | Code Style | JavaScript | Other, Generated code/Quote marks.
Since 2017.1.*, it is Settings | Editor | Code Style | JavaScript | Punctuation, Use <quote style> quotes in <new code/always>
This looks to be fixed with the 2016.2 release - there's now an option in the Editor --> Code Style settings where you can choose single/double quotes.