Descubrí que SqlBulkCopy es una manera fácil de hacer esto y no requiere que se escriba un procedimiento almacenado en SQL Server.
Aquí hay un ejemplo de cómo lo implementé:
// take note of SqlBulkCopyOptions.KeepIdentity , you may or may not want to use this for your situation.
using (var bulkCopy = new SqlBulkCopy(_connection.ConnectionString, SqlBulkCopyOptions.KeepIdentity))
{
// my DataTable column names match my SQL Column names, so I simply made this loop. However if your column names don't match, just pass in which datatable name matches the SQL column name in Column Mappings
foreach (DataColumn col in table.Columns)
{
bulkCopy.ColumnMappings.Add(col.ColumnName, col.ColumnName);
}
bulkCopy.BulkCopyTimeout = 600;
bulkCopy.DestinationTableName = destinationTableName;
bulkCopy.WriteToServer(table);
}