如果在AWS Sql Express中备份数据库到S3存储桶时遇到问题，可能有以下几种原因：

1. 权限问题：检查IAM用户的权限是否足够。如果你使用了不同的AWS账户作为S3存储桶和Sql Express的账户，请确保对S3存储桶的访问权限设置正确。

2. 传输协议问题：您可能尝试使用不受支持的传输协议，例如FTP或SMB。请使用支持的AWS SDK、CLI或其他适当的工具来传输备份数据。

以下是使用AWS SDK for .NET进行Sql Express备份和上传到S3存储桶的示例代码：

using System;
using System.Configuration;
using System.Data.SqlClient;
using Amazon;
using Amazon.S3;
using Amazon.S3.Transfer;

namespace AwsSqlBackupS3Example
{
    class Program
    {
        static void Main(string[] args)
        {
            // Set access key and secret access key for S3
            string accessKey = ConfigurationManager.AppSettings["AWSAccessKey"];
            string secretKey = ConfigurationManager.AppSettings["AWSSecretKey"];

            // Set S3 bucket region and name
            string bucketName = "your-bucket-name";
            RegionEndpoint bucketRegion = RegionEndpoint.USWest2;

            // Set Sql Server instance name and database name
            string instanceName = "your-instance-name";
            string dbName = "your-database-name";

            // Set Sql Server authentication
            string username = "your-username";
            string password = "your-password";

            // Set backup file name and path
            string backupName = dbName + "-" + DateTime.Now.ToString("yyyyMMddHHmmss") + ".bak";
            string backupPath = @"C:\Backups\" + backupName;

            // Set S3 object key name
            string objectKeyName = "Backups/" + backupName;

            // Create connection string
            SqlConnectionStringBuilder builder = new SqlConnectionStringBuilder();
            builder.DataSource = instanceName;
            builder.InitialCatalog = dbName;
            builder.UserID = username;
            builder.Password = password;

            // Prepare Sql backup command
            string backupCommand = "BACKUP DATABASE [" + dbName + "] TO DISK='" + backupPath + "'";

            // Create SqlConnection for the database
            SqlConnection connection = new SqlConnection(builder.ConnectionString);

            try
            {
                // Open database connection
                connection.Open();

                // Create SqlCommand to execute backup command
                SqlCommand command = new SqlCommand(backupCommand, connection);
                command.ExecuteNonQuery();

                // Upload backup file to S3
                TransferUtility transferUtility = new TransferUtility(accessKey, secretKey, bucketRegion);
                transferUtility.Upload(backupPath, bucketName, objectKeyName);

                Console.WriteLine("Sql backup completed and uploaded to S3 successfully.");
            }
            catch (Exception ex)
            {
                Console.WriteLine("Sql backup and upload to S3 failed: " + ex.Message);
            }
            finally
            {
                // Close database connection
                connection.Close();
            }
        }
    }
}

上面示例代码需要AWS SDK for .NET，可以使用NuGet来安装。注意，此示例代码只是演示，不应该直接用于生产环境。生产环境中，需要更加严格的安全措施，如使用IAM角色和KMS管理加密密钥等。