How can I display the number of related entries?
Try something like this:

&lt;form class="event-filter"&gt;
    &lt;label for="filter"&gt;Filter event: &lt;/label&gt;
    &lt;select id="filter" name="filter"&gt;
        {% for event in craft.entries.section('event') %}    
            {% set numEventBookings = craft.entries.section('booking').relatedTo(event).total() %}
            &lt;option value="i{{event.id}}"&gt;{{event.title}} ({{numEventBookings}} bookings)&lt;/option&gt;
        {% endfor %}
    &lt;/select&gt;
&lt;/form&gt;


But it'll generate one database query pr event, so it might be a bit inefficient, depending on your setup.