Hi Mark Rawson,
Only Bastion hosts with an IPv4 public IP, deployed in the Basic or Standard SKU, get a publicly resolvable DNS like bst-xxxx.region.bastion.azure.com
If your Bastion is Standard SKU private-only, it won’t have a public DNS name. Verify you have a static, standard public IP assigned. If missing, attach or create a new Public IP, save and wait 10–15 minutes for DNS propagation.
Confirm no NSG is blocking traffic on AzureBastionSubnet and the VM’s subnet/NIC allows inbound from Bastion on ports 3389 (RDP) or 22 (SSH).
Run nslookup bst-xxxx.region.bastion.azure.com
If successful, it should return the public IP address assigned to your Bastion.
If you have any further queries, let me know.