The syntax is generally the same as what would you would use in a SQL Where clause, without the "Where", so in this case, it would be
bindingSource.Filter = "Field <> NULL";
If you look at msdn docs for BindingSource.Filter you will see this:
"To form a filter value, specify the name of a column followed by an operator and a value to filter on. The accepted filter syntax depends on the underlying data source. If the underlying data source is a DataSet, DataTable, or DataView, you can specify Boolean expressions using the syntax documented for the DataColumn..::.Expression property."
Follow that link to see all the detailed rules