Can I hide the widget button on mobile devices?

There's no setting in the app to do this but you could hide the button by adding some CSS to your shop theme.

Use the template editor in your store admin and find the stylesheet in the Assets folder (for example,  style.css).

Add the following code and hit save:

@media only screen and (max-width: 320px) { 
  body > div#BIS_trigger { display: none !important; } 
}

Another option is to  add a link or button to your product page and use that instead of the widget button.