How to I style the Superfish accordion menu to have bars?
Seeing you are using responsive and that implies that you are size aware. You may find an icon set more elegant rather than a fixed sized background image.  

I load the font-awesome set into the site css anyway for use elsewhere. Therefor the icon's css are available sitewide.

If you look at the accordian settings for that sf menu, you'll see that you can edit that menu button (trigger) text. I found that though a text field, it does accept some html.

For example
Open Menu&lt;i class="fa fa-bars" aria-hidden="true"&gt;&lt;/i&gt;

gives you those the bars and they re-size as the button text does.