What is the MOST cost-effective method to establish this type of connection?

Explanations:

A client VPN is designed for individual remote users rather than for establishing a secure connection between on-premises environments and AWS. It is not ideal for corporate environments needing a stable, secure connection for internal systems.

AWS Direct Connect provides a dedicated network connection to AWS, but it is typically more expensive and is suited for high-bandwidth requirements, which is not the case here. Additionally, it requires more time and effort to set up compared to other options.

A bastion host on Amazon EC2 is used primarily to manage access to instances in a private network and does not create a secure connection between an on-premises environment and AWS. It is more about controlling access rather than establishing a direct network connection.

An AWS Site-to-Site VPN connection is the most cost-effective and quickest way to establish a secure connection between an on-premises environment and AWS, particularly for small amounts of traffic. It allows for secure tunneling over the Internet, making it suitable for low-bandwidth requirements.