I would like to stay in Bergamo Alta because it is closest to the sites we want to see. I know their vehicular traffic is somewhat limited and would like to find out the locations of the public parking areas. I am having trouble finding that information. Any suggestions would be appreciated.
Do a Google Maps search for "Parking in Bergamo, Italy" Looks like there's one at Piazza Mercato del Fieno and another at Piazza della Cittadella. What I don't know is where the ZTL is that you need to consider.
Try this one:
http://www.carservicefly.it/en/index.html
The thing I'd be concerned about it getting to ANY lot near or inside the Città Alta walls while avoiding ZTLs so I would make sure to get directions for doing that from the business. If you don't get much for other responses (honestly, Citte Alta really isn't a good place to take a car) here are a couple of fairly recent threads on TA about the subject:
https://www.tripadvisor.com/ShowTopic-g187830-i816-k12238778-Parking_in_Bergamo-Bergamo_Province_of_Bergamo_Lombardy.html
(see the last post by the Bergamo resident)
You might also search accommodations which offer parking as an amenity.
Wherever you are staying can advise you as to where to park. Here is the ZTL:
https://territorio.comune.bergamo.it/gfmaplet/?map=ZoneTL&highlightFeatures=ZTL%7C4%7CID_ZONA=2
If needing to park in Bassa, you can take the bus up to Alta, tickets from the shop in the station.
Several years ago we stayed at the exceptionally nice Hotel Petronilla and the parking was just on the street monitored by the property. It is not in La Citta Alta, but only a short cab ride away.
Buon viaggio,