One approach you can try is to define celltemplate for the column as shown below
<GridViewColumn x:Name="gdcol">
<GridViewColumn.CellTemplate>
<DataTemplate>
<TextBlock x:Name="txtbox" Text="{Binding Path}"/>
</DataTemplate>
</GridViewColumn.CellTemplate>
</GridViewColumn>
then in code where you want to update the target:
object obj = gdcol.CellTemplate.LoadContent();
TextBlock blk = obj as TextBlock;
BindingExpression exp = BindingOperations.GetBindingExpression(blk, TextBlock.TextProperty);
exp.UpdateTarget();
I have not tried the code, you can give it a shot.