What you are looking to do is reduce the results.
The key to this is to provide the same tools that users use for browsing in the search result, with a few tweaks to make them relevant. Avoid thinking of it as 'advanced search' as that's not the way users think - they just view it as one experience.
With the shopping sites I have worked on the common approach is to provide a faceted navigation that allows users to select attributes of a product. For women's dresses this is commonly colour, size, brand and price. The same principle applies to the mobile experience except it makes sense to have the filters hidden. There are multiple ways to call these up, a simple concertina, a sliding approach where it is to the left or a full screen solution if you need to show more. If you look at the John Lewis mobile website I did the first version of a few years ago (m.johnlewis.com) I used a full screen approach. I think I'm more likely to use a side menu or some other method now but it still works as it is.
What ever you do don't use a gear icon as that relates to settings NOT navigation - which essentially what we are looking at here. Search and navigation should be seen as one and the same thing as much as possible.