Ordinary databinding doesn't generally allow for expressions. Under the hood the datagrid is using reflection (rather the executing code the way DataBinder.Eval does on an ASP.NET page) to find the property that you specify to bind to a column. To do what you want it would need to evaluate the binding as an expression, work out that you were looking for a parent -> child relation, and then reflect down to that level. AFAIK the inbuilt databinding on the grid is too dumb to know how to do this.
I've had the same issue recently, and my solution was to do a LINQ projection and bind that to the grid instead. Something like the following (in C# because I'm not comfortable with the LINQ syntax in VB):
IList<ClassA> listOfClassAObjects = GetMyListOfClassAObjectsFromSomewhere();
var projection = from ClassA a in listOfClassAObjects
select new { SomeProperty = a.SomeProperty,
SomeOtherProperty = a.SomeOtherProperty,
SomePropertyFromB = a.ClassB.SomeProperty };
datagrid.DataSource = projection;
datagrid.DataBind();
You'll get back a list of anonymous types containing that projection, and you can bind the appropriate column to SomePropertyFromB
.
For extra encapsulation (if you do this a lot) put the projection into an extension method so you can do something like
var data = GetMyListOfClassAObjectsFromSomewhere().ProjectionForDataGrid();
datagrid.DataSource = data;
datagrid.DataBind();