For using COM (aside from VBA), you have to do a bit more work to instantiate the AecScheduleApplication. You must allow AutoCAD to instantiate the object so that it knows which application is should get the schedule app from.
Here is some code that should get you started (sorry, c#):
AcadApplication app = (AcadApplication)Application.AcadApplication;
AecScheduleApplication sched = (AecScheduleApplication)app.GetInterfaceObject("AecX.AecScheduleApplication.4.7");
When working with ADT, you will find that you need to use this pattern above for instantiating certain ADT objects. For example, AecAnchorTagToEnt. The 4.7 corresponds to the COM library version, in this case for ADT 2006. You'll need to adjust this number for the version of ADT you are using. When you are getting null object errors, give this a try.