Collapsible Search Bar
If I understood you correctly:
You have exposed filter in block, which have for example two fields, search by title and checkboxes.

So you can use: https://www.drupal.org/project/better_exposed_filters


After installing module: change Exposed form style from Basic to Better Exposed Filters
Click to BEF Settings
Check Enable secondary exposed form options
Expand yours fields what you need to hide before type in search box and check this: This is a secondary option
Use jQuery:

$("input.yourSearchBox").keyup(function(){

    $(".views-widget-filter-secondary a").trigger('click');

});