Generally forms are the same as Bootstrap forms. Examples and usages of forms can be found at Bootstrap documentation.
<div class="search-box inline-filters">
<form>
<!-- search bar row -->
<div class="row form-inline">
<div class="col-sm-10 col-xs-8 form-group with-filter">
<input type="text" placeholder="Search" class="form-control"><a href="#" data-toggle="tooltip" data-placement="top" title="Filter" class="toggle-filter"><i class="icon oi-filter"></i></a>
</div>
<div class="col-sm-2 col-xs-4 form-group">
<input type="submit" value="Submit" class="btn btn-small btn-skin-red btn-block">
</div>
</div>
<!-- filters row -->
<div class="row filters"><a href="#" class="clear-selectize">Clear Filters</a>
<div class="col-sm-6">
<div class="form-group">
<label>Publication Type:</label>
<select data-placeholder="Select Types..." multiple="multiple" class="selectize">
<option value=""></option>
<option value="Journal Article">Journal Article</option>
...
</select>
</div>
<div class="form-group">
<label>Year:</label>
<select data-placeholder="Select Year" multiple="multiple" class="selectize">
<option value=""> </option>
<option value="2000">2000</option>
...
</select>
</div>
</div>
<div class="col-sm-6">
<div class="form-group">
<label>Category:</label>
<select data-placeholder="Select Types..." multiple="multiple" class="selectize">
<option value=""></option>
<option value="Physics">Physics</option>
...
</select>
</div>
</div>
</div>
</form>
</div>
This consists of two visually distinct sections; 1. The search bar .row
2. Filters .row