Having a parent respond to a child's event
It's really hard to judge if exposing selector is the &quot;right&quot; thing to do without reviewing more of your source code.
Also, it depends on your architecture design. If you're using a Model View Controller approach, then yes. Elements associated with the view will be exposed.
Check out some of the examples for Backbone.js.
Here are some other factors that come into play:

Coding standards
size of your source
how strictly you're required to follow Object Oriented Programming, OOP.
who will maintain your code.

The code you provided looks great. As long as you produce consistent readable code that has a good level of data abstraction and works, then you shouldn't worry about the small details.
If you're still concerned about it though then just create an adapter for the .bind().
Old Code:
ordersSearchResult.selector.bind('searchResultLinkClicked', function () {
    ordersEditDisplay.hide();
    ordersSearchDisplay.fadeIn();
});

New Code:
...
OrdersSearchResult.prototype.bind = function(eventName, fn ){
    this.selector.bind( eventName, fn );
};
...
var ordersSearchResult = new OrdersSearchResult();
ordersSearchResult.bind('searchResultLinkClicked', function () {
    ordersEditDisplay.hide();
    ordersSearchDisplay.fadeIn();
});    

Here are a few additional tips.
1) Name variables and properties based on their overall purpose and type.

Programmer A: There's a problem with orders in your code.
Programmer B: Which one? Are you talking about the function, jQuery object, element id, or something else?

To avoid this situation, create unique names assuming the language is case insensitive.
Old code:
$(function Orders() {
    &quot;use strict&quot;;
    var orders = $('#Orders');
    ...

New code:
$(function OrdersFunc() {
    &quot;use strict&quot;;
    var $orders = $('#OrdersTable');
    ...

More info here: &quot;How to name variables&quot;
2) Add the dollar sign as a prefix for jQuery variables.
It would make more sense to rename selector as $el.
3) Try not to create method names that are the same from a different library API.
ordersEditDisplay.hide() sounds like ordersEditDisplay returns a jQuery object, but that isn't the case.
Instead of ordersEditDisplay.hide();, try ordersEditDisplay.hideView();
4) Use the Singleton Pattern or an object literal to create a namespace.
Great examples can be found here
Final Code:
var mySite = {};
mySite.Orders = {};
mySite.Orders.init = function() {
    &quot;use strict&quot;;
    var $orders = $('#OrdersTable');

    var ordersSearchResult = new OrdersSearchResult();
    var ordersSearchDisplay = new OrdersSearchDisplay();
    var ordersEditDisplay = new OrdersEditDisplay();

    ordersSearchResult.$el.bind('searchResultLinkClicked', function () {
        ordersEditDisplay.hideView();
        ordersSearchDisplay.fadeInView();
    });
};
$(mySite.Orders.init);