So I've found the answer to my own question, and figure I'll post it for the sake of others and my future self.
The settings used by the bundle installer's "-s" "-g" and "-d" options are stored in a database (not sure the format) packaged with VMware. This database can be dumped using
./vmware-installer.bundle --dumpDB ${PATH_TO_OUTPUT_XML}
This will create a new XML file at ${PATH_TO_OUTPUT_XML}. You can read the XML directly, but I found it much more manageable to use xmllint to parse it a bit. The table of interest is called "settings"
xmllint <(xmllint ${PATH_TO_OUTPUT_XML} | grep "<table>settings") --shell
This will drop into an xmllint shell with only the settings table read in
/ > cat table/row
[OUTPUT]
/ > exit
The [OUTPUT] should contain every setting used by the installer, including the component name, so I discovered the relevant settings to automate installation:
| Component Name | Key | Value |
|---|
| vmware-player-app | softwareUpdateEnabled | [yes/no] |
| vmware-player-app | dataCollectionEnabled | [yes/no] |
| vmware-workstation-server | hostdUser | [a username] |
| vmware-workstation-server | datastore | [a path on disk] |
| vmware-workstation-server | httpsPort | [a port number] |
| vmware-workstation | serialNumber | [your license key] |
Setting each of these with "./vmware-installer.bundle -s ${COMPONENT_NAME} ${KEY} ${VALUE} ... --eulas-agreed" was almost enough on its own, except the installer will still prompt:
For a license key, but the default value is now what was set using the "serialNumber" setting.
Press enter to begin installation
To get around this I piped yes '' (that's two single quotes for a blank string) to the installer, the final command looks like:
yes '' | ./vmware-installer.bundle -s vmware-player-app softwareUpdateEnabled no -s vmware-player-app dataCollectionEnabled no -s vmware-workstation-server hostdUser ${USERNAME} -s vmware-workstation-server datastore ${PATH} -s vmware-workstation-server httpsPort 443 -s vmware-workstation serialNumber ${LICENSE_KEY}
This command performed a fully automated installation, there was still some output to the screen, but I can live with that and can always redirect it to /dev/null if need be.
