INSERT object or UPDATE if it already exists using BulkCopy (C#, SQL)

I'm trying to update a table with a List<T>. I created an EnumExtension class and created a method which converts my Enumerable to a DataTable:

public static DataTable AsDataTable<T>(this IEnumerable<T> data)...

And then I started creating a method which should use BulkCopy to insert or update my table, using the enumerable. Right now, it's written like this:

public void BulkInsertOrUpdate(DatabaseEnum database, IEnumerable<Object> enumerable, string TableName)
    {
        var connection = this.GetSqlConnection(database);

        var transaction = connection.BeginTransaction();

        using (var bulkCopy = new SqlBulkCopy(connection, SqlBulkCopyOptions.Default, transaction))
        {
            bulkCopy.BatchSize = 100;
            bulkCopy.DestinationTableName = TableName;
            try
            {
                bulkCopy.WriteToServer(enumerable.AsDataTable());
            }
            catch (Exception)
            {
                transaction.Rollback();
                connection.Close();
            }
        }
        transaction.Commit();
    }

(OBS: Method GetSqlConnection creates and opens my connection using the appropiate connection string.)

But I don't know how to create the update feature. Is there a simple way to do so, with an efficient code? I'm fond of BulkCopy, but I can try another method, hopefully not hurting my architecture (and, ultimately, I'll have to make this sacrifice if I can't find a way).

Thanks for your attention, I'm ready to answer doubts about my situation.