Cross-Platform Deployment Tasks in Bamboo
There isn't a common protocol that exists on all the platforms for deployment.  However, if you get an SSH server onto the windows platforms then you can use the same mechanisms in Bamboo to do the deployment, and potentially even use the same keys to secure it all.
Windows SSHD - There are a few alternatives (https://serverfault.com/questions/8411/what-is-a-good-ssh-server-to-use-on-windows).  Freesshd you can get administrator level access - been successfully using it with thousands of machines as old as WinXP for years.
The Bamboo SCP task can be used to do the staging to the remote servers - once you have SSH remote access to all your targets.

You can use the Bamboo SCP task to upload files from Bamboo directly to a remote server as part of a Bamboo job. The SCP task is able to copy multiple files and preserves the directory structure for the copied files.

And Bamboo SSH task can then do post deployment install steps, running scripts relevant to the platform.

You can use the Bamboo SSH task to execute a SSH command on a remote computer as part of a Bamboo job.