Private transfer Venice to Trieste

You are looking at train schedules too far out—-the October schedule is not complete yet. If you look at the schedule for next week or next month, you will see trains departing Venezia Santa Lucia to Trieste at 9:39, 10:01, 10:11, 10:39, 1201, 12:39, 13:39, 14:01 and on throughout the afternoon.

https://www.trenitalia.com/en.html

Not sure what website you were using, but Trenitalia, the Italian rail line, won't have issued their train schedule for October. You won't see the full schedule till some time in June. For a good idea of trains, go to the Trenitalia website, pick a week within the next month (same day of the week you plan to travel). On a random day next month I saw trains every half hour, if not more frequent around rush hours.

I've not been to Trieste so am not familiar with the rail schedule between Venice and that city, but I'd say you are looking way too early for October departures. There's a Europe-wide schedule change every year in early June. Although the schedules tend not to change very much, that means you are not seeing most of the trains. To get a better idea of your options, search trenitalia.com for the right day of the week in early May. That will be pretty close to what you will see for your travel date when October schedules are loaded later.

Most of the Venice-Trieste trains are regionals. The few departures that put you on a faster train between Venice-Mestre and Trieste don't necessarily save time, because you have a layover at Mestre for the change of trains. The regional trains have no seat assignments and don't sell out, so there's no reason to buy those tickets early. You'll want to check the travel time, though, because it ranges from 2 hr. 5 min. all the way up to 3 hr. 49 min.

The cruise line does not offer a solution?

I took that train in the opposite direction last August. I bought the tickets 10 minutes before departure. You don't need to book this in advance, there is no benefit.