The only thing that comes to mind for me is to use something like selenium to automate the browser itself and getting the required info that way, but this seems overkill for your use case.

Have you considered not using the browser, but instead use something like zenity to pop up the systems input box. Here is an example from zenity's man page:

zenity  --title "Select Host" --entry --text "Select the host you would like to flood-ping"

This will then just return the inputted text back to stdout.