By default, the BottomSheet will take up half the screen:

  onPressed: () {
    showModalBottomSheet(
      context: context,
      builder: (context) => AddTaskScreen(),
    );
}

For certain screen sizes, this may mean the Add button is obscured. Setting the isScrolledControlled property to true you can make the modal take up the full screen:

  onPressed: () {
    showModalBottomSheet(
      context: context,
      isScrollControlled: true,
      builder: (context) => AddTaskScreen(),
    );
}

To have the AddTaskScreen sit just above the keyboard, you can wrap it inside a SingleChildScrollView, which determines the padding at the bottom using a MediaQuery.

onPressed: () {
  showModalBottomSheet(
    context: context,
    isScrollControlled: true,
    builder: (context) => SingleChildScrollView(
      child:Container(
        padding: EdgeInsets.only(bottom: MediaQuery.of(context).viewInsets.bottom),
        child: AddTaskScreen(),
      )
    )
  );
}