Nodes are not assigned public IP. If you have accessible VM in the same VNET as worker nodes, then you can use that VM as jump host and connect the worker via private IP.
Alternatively public IP can be assigned to a worker node. This readme shows how to do that.
find out the resource group that AKS created for the node VMs
az group list -o table
list resources in the group and find the VM you want to access
az resource list -g MC_kubernetes_kubernetes-cluster_ukwest -o table
show parameters of that VM, see for example: "adminUsername": "azureuser"
az vm show -g MC_kubernetes_kubernetes-cluster_ukwest -n aks-agentpool1-18549766-0
create the public IP
az network public-ip create -g MC_kubernetes_kubernetes-cluster_ukwest -n test-ip
find out correct NIC where to add the public IP
az network nic list -g MC_kubernetes_kubernetes-cluster_ukwest -o table
find out the name of the ipconfig within that NIC
az network nic ip-config list --nic-name aks-agentpool1-18549766-nic-0 -g MC_kubernetes_kubernetes-cluster_ukwest
modify the ipconfig by adding the public IP address
az network nic ip-config update -g MC_kubernetes_kubernetes-cluster_ukwest --nic-name aks-agentpool1-18549766-nic-0 --name ipconfig1 --public-ip-address test-ip
find out what the allocated public IP address is
az network public-ip show -g MC_kubernetes_kubernetes-cluster_ukwest -n test-ip
then finally connect with SSH
ssh azureuser@<public ip address>
I had the same problem (got to the public key error). To solve I just followed the steps detailed here: https://github.com/MicrosoftDocs/azure-docs/issues/7463
-regenerate SSH keys
-In the portal, select an AKS node VM and reset password
-Select Reset SSH public key, enter the username azureuser by default, and paste in the new public key id_rsa.pub
-Create SSH connection as described in the doc