Nakonec se mi to podařilo takto
using (var bulkCopy = new SqlBulkCopy(ConfigurationManager.ConnectionStrings["ConnectionString"].ConnectionString, SqlBulkCopyOptions.KeepNulls & SqlBulkCopyOptions.KeepIdentity))
{
bulkCopy.BatchSize = (int)DetailLines;
bulkCopy.DestinationTableName = "dbo.myTable";
bulkCopy.ColumnMappings.Clear();
bulkCopy.ColumnMappings.Add("SourceColumnName", "DestinationColumnName");
bulkCopy.ColumnMappings.Add("SourceColumnName", "DestinationColumnName");
bulkCopy.ColumnMappings.Add("SourceColumnName", "DestinationColumnName");
bulkCopy.ColumnMappings.Add("SourceColumnName", "DestinationColumnName");
.
.
.
.
bulkCopy.ColumnMappings.Add("SourceColumnName", "DestinationColumnName");
bulkCopy.WriteToServer(datatable);
}