I just launched a fresh Bitnami Magento instance in Google and could copy a file from my local computer to the remote instance
It's important to mention that I didn't drop the file into the apps, htdocs or stack folder, I did it over the rest of the files of the /home/bitnami folder. If the file I want to move from my local computer is dropper over any of those folders, I obtained a permission denied error message
If that doesn't work, you could download the theme from the Magento instance, you could access the instance using a SSH connection and then run the wget command with the URL you want to download
wget "URL TO DOWNLOAD THE THEME"
Let us know if you have any questions