Can I do route 53 private hosting on a server connected to a bastion host?

Yes, you can use a bastion host to connect to an external server through a private hosted zone in Route 53. Here are the high-level steps to set this up:

1. Set up a private hosted zone in Route 53 for your domain.
2. Set up your DNS records in the private hosted zone to point to your external server's IP address.
3. Configure your VPC to use the private hosted zone for DNS resolution.
4. Set up a bastion host in your VPC and configure it to allow SSH or RDP access to your external server.
5. Connect to the bastion host using SSH or RDP, and then connect to the external server from there.

By using the private hosted zone, the DNS resolution for your domain will be handled within your VPC, so the requests won't leave your network. The bastion host will act as a jump server to allow you to connect securely to the external server without exposing it to the internet directly.