The correct service for establishing a high-bandwidth, private connection that bypasses the public internet is called Direct Connect. This option enables companies to create a dedicated networking connection to their cloud resources, which is particularly important for workloads that require enhanced privacy, consistent network performance, and high data transfer rates. Alternatives like API Gateway are designed to manage APIs and not to create network connections. Similarly, while VPC Peering and VPN help to connect networks, they do not provide a dedicated physical connection with the consistent, high capacity that Direct Connect does, and may rely on the public internet.