Filling a DataSet or a DataTable from a LINQ query result set

Make a set of Data Transfer Objects, a couple of mappers, and return that via the .asmx.
You should never expose the database objects directly, as a change in the procedure schema will propagate to the web service consumer without you noticing it.

To perform this query against a DataContext class, you'll need to do the following:

MyDataContext db = new MyDataContext();
IEnumerable<DataRow> query = 
    (from order in db.Orders.AsEnumerable()
        select new
        {
            order.Property,
            order.Property2
        })
    as IEnumerable<DataRow>;
return query.CopyToDataTable<DataRow>();

Without the as IEnumerable<DataRow>; you will see the following compilation error:

Cannot implicitly convert type 'System.Collections.Generic.IEnumerable' to 'System.Collections.Generic.IEnumerable'. An explicit conversion exists (are you missing a cast?)

As mentioned in the question, IEnumerable has a CopyToDataTable method:

IEnumerable<DataRow> query =
    from order in orders.AsEnumerable()
    where order.Field<DateTime>("OrderDate") > new DateTime(2001, 8, 1)
    select order;

// Create a table from the query.
DataTable boundTable = query.CopyToDataTable<DataRow>();

Why won't that work for you?