Begin by pulling the desired Docker image from Docker Hub to your local machine. Use the Docker CLI command:
```bash
docker pull :
```
Replace `:` with the specific image and tag you wish to download.

Create a new container from the pulled image and extract the filesystem. Run the container in interactive mode:
```bash
docker create --name temp_container :
```
Then, export the filesystem:
```bash
docker export temp_container -o image_filesystem.tar
```

Ensure the AWS Command Line Interface (CLI) is installed and configured on your local machine. If not already installed, follow the installation instructions:
```bash
pip install awscli
```
Configure the AWS CLI with your credentials:
```bash
aws configure
```
Provide your AWS Access Key, Secret Key, default region, and output format when prompted.

Extract the contents of the `image_filesystem.tar` to a local directory. Use the following command:
```bash
mkdir image_filesystem && tar -xvf image_filesystem.tar -C image_filesystem
```
This prepares the files for upload to S3 by extracting them to a directory.

Navigate to the extracted directory and organize the files as necessary. Ensure the directory structure is ready for direct upload to your S3 bucket.

Use the AWS CLI to recursively upload the directory to your specified S3 bucket:
```bash
aws s3 cp image_filesystem s3://your-bucket-name/ --recursive
```
Replace `your-bucket-name` with the name of your target S3 bucket. This command uploads all files and directories recursively.

After confirming the data is successfully uploaded to S3, remove the temporary container and local files to free up space:
```bash
docker rm temp_container
rm -rf image_filesystem image_filesystem.tar
```
This ensures your local environment is clean and free of unnecessary files.
By following these steps, you can effectively move data from Docker Hub to an Amazon S3 bucket using native tools and commands.