This is a very impressive web resource
It doesn't mention travel passes for the over 60s though.
http://orbis.stanford.edu/#

I couldn't load the page in my IE browser until today (just upgraded it) so I've just been in and had a gander.

It is quite impressive, at least as a general guide to how things and people might have been moved around in times of general political stability, secure economy with consistent currency valuation, clear and consistent differences between social classes within the state, and clear distinction between military and civilian use and control of transport media.

I'm just wondering if such a time ever existed?

There probably never has been such a time in any society. Even in the long history of ancient Egypt there were constant upheavals. The closest there was to an era of stability as described above would probably have been the Twelfth Dynasty in the Middle Kingdom which lasted around 200 years.

With regard to Rome, then the Second Century and the era of the Nerva-Antonine dynasty with its 'Five Good Emperors' would come closest to this. Intriguingly that also coincides with a similarly stable era in Chinese history - the Latter Han dynasty. There were even tentative links during this period between the 2 civilisations (in both directions) sometimes called 'embassies' but more likely just glorified trade missions.