Connect Powerbi with AWS RDS with no public accessibility

Yes - Create an EC2 Windows server instance and install & configure on-premise power bi gateway on same subnet you hosted the bastion server.

Optional: And in Power BI Desktop change hard-coded server name in mysql queries with newly created ServerName Parameter and re-publish the report.

Now in Power BI Service add new MySQL datasource (main servername) under Settings=> Manage gateways using with database user credentials.

After configuring the gateway you should able to schedule the refresh intervals. 

If you want to connect to MySQL workbench on your local machine effectively - you can change hosts file under 'C:\Windows\System32\drivers\etc' with administrator rights

# localhost name resolution is handled within DNS itself.
# 127.0.0.1 localhost
# ::1 localhost

127.0.0.1 localhost
127.0.0.1 xyz::mysql
127.0.0.2 localhost
127.0.0.2 abc::mysql

SSH Tunnel

ssh -L 3306:xyz::mysql:3306 -L 127.0.0.2:3306:abc::mysql:3306 [email protected]

MySQL Workbench - server connections

Hostname: 127.0.0.1; Port: 3306 for connecting to xyz::msql server

Hostname: 127.0.0.2; Port: 3306 for connecting to abc::msql server

Hope this helps.