Train Padova to Bolzano

If you use all regional trains, you do not need to reserve as there are no seat reservations and no advance purchase discounts.
The main station in Bolzano, close to the bus station is simply "Bolzano Bozen".

Could I purchase the ticket from Padua to Bolzano the day before...and would it be good for the entire day, giving me options for any train throughout the day?

No. A ticket bought at the station, either from the ticket window or a ticket machine, has a certain time limit to complete the trip once the ticket is validated in the stamping machine on the platform. You do this just before boarding the first train at Padova. This time limit is based on the fastest time the trip could reasonably completed. Any grace time varies by region.

Edit, I finally located the Conditions of Carriage, only available in Italian. with the help of google translate:

From the moment of validation, the ticket is valid for 4 hours, except for different periods of use
provided for by individual regional/provincial tariff provisions.
The trip must, therefore, be completed within the aforementioned validity period.
However, the passenger who is on the train at the end of the validity of the ticket can continue the journey
already started up to the destination station without making intermediate stops. Where the solution of
journey purchased presupposes a train change, the passenger can also complete the journey a
condition that you use the first available train at the changeover station.

Sam's right, these are both regionale trains so no need to reserve just show up for the train you want. You can use a ticket window or machine or the Trenitalia app.

I advocate for downloading the app and buying ticket that way. Look up schedules, track trains and literally buy the tickets as you get on the train if it's already there when you show up.

I downloaded the app on the advice of a friend but didn't think I'd use it for tickets until we showed up at La Spezia station 15 minutes before the train left and all the tickets machines had huge lines. I literally bought tickets as the line moved two spaces and never looked back.

Some people advocate saving screenshots of the tickets for the conductor "just in case" which I guess isn't a bad idea but it was never an issue for us.

Have a great trip,
=Tod

Carol,

Some of the trains on that route will be Freccia trains heading up the Brenner Pass, and those do have compulsory reservations. Those are slightly faster than the Regionale trains, but use whichever departure time works best for your schedule. I often buy tickets the day prior to travel when the stations and ticket machines are not too busy, but these days I could also buy using my mobile phone. If travelling via Regionale, all I have to do is validate the ticket prior to boarding the train the next day.

When you arrive at Verona Porta Nuova station, as I recall there are two parts to the station and the trains going north depart from a different section. I can't remember the details.

The Bolzano/Bozen station is an easy walk to the bus depot. You might want to have a look at Google Maps to get a general idea of the route to follow. As I recall, the bus makes several stops in the Castelrotto area, so be sure to watch for your stop.

You can't reserve a ticket on a train with no reserved seats. You can only pay in advance and, if your plans are set, have one thing less to worry about.

Of course you can get tickets online on the day of travel, for example at the hotel before going to the station. Or at the station if you have data connection.

Could I purchase the ticket from Padua to Bolzano the day before...and would it be good for the entire day

Yes, that's how paper regionale tickets bought at the station work. You pick a day of travel and a route, not a specific train. Otherwise the process of validating paper Regionale tickets would be totally pointless.

But as you have been told, these trains can't sell out. You could enjoy the same flexibility getting an e-ticket online up to 5 minutes before boarding. Without wasting time at the station the day before.

Edited because the message below is right

Don't cut it too close if you plan to buy your ticket shortly before departure. At some point (it might be 5 minutes before scheduled departure), the app won't sell you the ticket, and I don't think the vending machines will, either. I am the queen of just-in-time arrival at train stations, and it was frustrating to be standing in a small station before the train even arrived and be unable to buy a ticket. Otherwise, the app is great.

Thank you ALL so much.

Tod the Hiredman & Dario: Yes, we have the Trenitalia App on our phones which we used it last year. And yes, we both have data connection. (Unrelated, but we realize how useful it is for both of us to have it after my husband's phone was stolen one year).

Ken: Thanks for the info on the Freccia trains heading to Brenner Pass. That explains why some of the times are shorter than others between Padova and Bolzano. Now I know we have the option to purchase tickets the day before....and just remember to validate prior to boarding.
Thank you also for alerting us to the Verona Port Nuova station...to not panic and read the boards and get to the right station/platform. Yes...to Google Maps for looking at the area around the stations.

Acraven: Thanks for the "heads up" about not waiting until the last minute to purchase tickets. That would be scary...to be on board and not be able to purchase. (On a prior trip to Switzerland, using the SBB App, we were able to purchase tickets AFTER we were seated on the train)
All of you have lessened my anxiety.
We need to get to Ortisei in time for our half-board meal that evening.

Carol,

You may already know this, but paper tickets for the Freccia trains do not have to be validated, as they come with compulsory seat reservations which are specific to train, date and departure time.

Question about the Verona Port Nuova Station:
Ken mentioned that there are 2 parts to the station, with trains going north departing from a different section. So...I did a bit of searching, first on Google...then on Man in Seat 61. Seems like the regional train arrive and depart from a different area than the ones heading to Milan or Rome or the Brenner Pass. He also mentions the 2 sections connected by a "subway."
Does "subway" refer to just an underground passage for foot traffic...or "subway" with some type of transport connecting the 2 sections? Hoping for some clarification...also, that will help us plan to allow sufficient time to connect with trains heading to Bolzano.
Thanks!

*bumping this up, hoping someone can answer my question about the Verona Train station.

“Subway” refers to an underground passage-pedestrian

Carol,

Just to confirm, yes the "subway" was a pedestrian walkway. You may have already looked at this website - https://www.seat61.com/stations/verona-porta-nuova.htm#Which_platform . As mentioned in the article, it's a really good idea to confirm the Binario with the local departure boards in the station, as they sometimes change.