gistfile1.cs

private readonly string _storageUrl;
private readonly string _serverName;
private readonly string _sqlUsername;
private readonly string _sqlPassword;
private readonly string _storageAccountName;
private readonly string _storageKey;
private readonly string _storageContainer;

public string Backup(string database, string[] selectedTables, out string filename)
{
    var time = DateTime.Now;
    filename = string.Format("{0}-{1}-{2}-{3}-{4}-{5}.bacpac", database, time.Year, time.Month, time.Day, time.Hour, time.Minute);
    var credentials = new BlobStorageAccessKeyCredentials() { StorageAccessKey = _storageKey, Uri = StorageUrl + filename};

    var connectionInfo = new ConnectionInfo();
    connectionInfo.ServerName = _serverName;
    connectionInfo.DatabaseName = database;
    connectionInfo.UserName = _sqlUsername;
    connectionInfo.Password = _sqlPassword;

    var se = selectedTables != null && selectedTables.Any();

    // create the request
    var request = WebRequest.Create(string.Format(ServiceUrl, "SelectiveExport"));
    request.Method = "POST";
    request.ContentType = "application/xml";

    // tables specified, do selective export
    if (se)
    {
        // select to export the names listed
        var tables = selectedTables.Select(a => new TableName() {Name = a});
        // this can be done for just the schema as well
        //var tables = new List<TableName>() {new TableName() {SchemaName = "dbo"}};
        var selectiveExport = new SelectiveExportInput() { ConnectionInfo = connectionInfo, BlobCredentials = credentials, Tables = tables.ToArray() };

        using(var stream = request.GetRequestStream())
        {
            var dcs = new DataContractSerializer(typeof(SelectiveExportInput));
            dcs.WriteObject(stream, selectiveExport);    
        }
    }
    // full export of database
    else
    {
        var exportInput = new ExportInput() { ConnectionInfo = connectionInfo, BlobCredentials = credentials };

        using (var stream = request.GetRequestStream())
        {
            var dcs = new DataContractSerializer(typeof(ExportInput));
            dcs.WriteObject(stream, exportInput);
        }
    }

    // make the post
    using (var response = (HttpWebResponse)request.GetResponse())
    {
        if (response.StatusCode != HttpStatusCode.OK)
        {
            throw new HttpException((int)response.StatusCode, response.StatusDescription);
        }

        var sr = new System.IO.StreamReader(response.GetResponseStream());
        var result = sr.ReadToEnd().Trim();

        // read out the tracking code, so you can lookup status
        var xml = XDocument.Parse(result);
        var node = xml.Descendants().First();
        return node.Value;
    }
}