I' dont use GWTP, but I guess the following is ok.
@Inject private EventBus eventBus
should work (if you don't use it in SearchDialogBox constructor right away).
Otherwise try to find out which class in GWTP extends com.google.gwt.inject.client.Ginjector. Assuming it is called "MyInjector" just write :
private EventBus eventBus = MyInjector.INSTANCE.getEventBus();