When should I buy train ticket from Bolzano to Venice?

There is only one train route, regardless of the speed of the train or the number of stops. (And the scenery certainly becomes more "pedestrian" after you make the connection at Verona toward Venice.)

If you don't want to commit to getting your group of 6 onto a specific train, then full-fare tickets purchased in the station would not cost more than about $50 per person in the cheapest 2nd class/economy seating on the fastest trains.

Tickets purchased in advance can be cheaper, or a regional train from Verona can be cheaper, and either might also give you a better shot at finding seats together. www.trenitalia.com will show you all the price options.

Buy the tickets now . As is usually the case , the closer you get to your travel date the higher the price for the tickets . Right now tickets are on sale for as low as 19EU and regardless of the specific train , the trip is about three hours

Thank you, I went in to book it at the €119 for the six of us, but it said error code, rate not available. We had to book the first class fare. Now we need to book from Venice over to Monterrosso, on June 5th. Is the train station simply Monterrosso? I have a difficult time finding the actual train station names. If so, I see it’s a long trip 5-6 hrs by train. Any suggestions on an economical ticket? As a US citizen it doesn’t look like I can take advantage of the “young” rates, is that correct?

Did you register on the Trenitalia site when attempting to book your seats ? Things can get gummed up if you don't . Also , Trenitalia can be a bit temperamental at times , so here is a site that is easier to use , with the same prices as the original seller - https://en.wikipedia.org/wiki/Trainline_EU

I think you want just plain "Monterosso".

When traveling to small places like that, at least part of your trip will be on a regional train. Even if a fast train passes tnrough a small town, it will not stop there. (That's one reason it's a fast train.)

For some trips in Itaky you'll see significant price variations between departure times because you have a choice between itineraries that are mostly on fast trains and itineraries that are mostly or entirely regional. I believe there may be some differences in the presence or quality of the air conditioning on regional trains vs. Frecce, so that's something to pay attention to for summer travel. Otherwise, I look carefully at the total travel time for each option. Sometimes the time you gain while riding on the expensive fast train disappears during the connection you have to make to the slow train. You can end up paying substantially more but not arrive faster--or at least not enough faster to matter.

Let me spread some light:

1. fares do not increase indefinitely. Purchasing on the same day of travel you'll pay the full price, that is always displayed in advance on official sites and that is called BASE on trenitalia.com/tcom-en and FLEXI on italotreno.it/en.
2. BASE and FLEXI are the most expensive tickets AND the most flexible ones. A BASE ticket can be exchanged for free up to one hour after the departure of the booked train; for Italo's FLEX the limit is 2 hours
3. Don't waste time trying to register on trenitalia.com. You don't need it and I doubt you could do it easily without an address in Italy.
4. To get the discount for young people you must purchase a discount card called Cartafreccia Young. To make it break-even you must use it many times.
5. Trenitalia.com isn't temperamental anymore, but if there aren't 6 tickets left at the same price, it doen't mix different fares to make you save money. You had to make 2 separate purchases (4+2) noting down the car # assigned to the first batch of tickets. Note that If you pick the CartaFreccia Young fare without entering the number of your CartaFreccia Card, the site won't let you finish the order
6. you'd better tell your bank you are going to buy something abroad, to avoid problems.
7. Turn off the auto-translate option on Chrome if you want to try to register on italian sites
8. Station names always begin with the name of the city/town/village. Of course I mean the italian name: Venezia, not Venice. When that place boasts more than one station, the city name is followed by a name like Centrale or Porta X or Saint Y (the parish church that gave its name to that district). All stations can be found on google maps.
9. Monterosso has only one station, but there is another village in southern Italy called Monterosso Marche.