Monopoli to Salerno

Have you checked Trenitalia?
Pretty sure you will have to change in Bari, then Naples

Or at least 1 change in Caserta

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

It's a long trip! I've not done it directly, but I've done each part by train.
There is a direct Freccia originating at Lecce that you could take between Monopoli and Caserta, and then change there for Salerno.
It may give you more options to get a regional fast train to Bari, then the Freccia.

There are no direct routes departing from Bari or Monopoli. By the current Trenitalia schedules, all the 1-change options are via Bologna and take more than 10 hours.

If I were you, I'd take a Regionale train from Monopoli to Bari centrale. Once you are there, it's a 5 minutes walk to the bus station to the back of the building where you can take the direct Marozzi SitaSud bus to Salerno that departs at 13:55: https://shop.marozzivt.it/en/from/Bari/today/to/Salerno/

Thank you for all the suggestions! I did a little more digging while I was waiting for responses and it seems there is a bus - Itabus - that goes from Bari to Monopoli in 4 hours. I have never taken this bus line (only Flixbus) and may be an option or the train Bari to Naples and switch.

Bologna?? That must be a typo

The one change route thru Caserta takes 6h 16m

The bus from Bari is 4 hours

The one change route thru Caserta takes 6h 16m

That's one change from Bari, two changes from Monopoli. The only way to change once from Monopoli is going north up to Bologna and then south to Salerno.

that goes from Bari to Monopoli in 4 hours.

I guess you mean 4 hours from Bari to Salerno

there is a bus - Itabus

As I wrote above there is also the Marozzi Bus.

Do you know where Bologna is?
Why in the world would you need to travel halfway across the country and back?

Trenitalia shows a journey with just one change from Monopoli - change in Caserta
7:03 fast train change to regional
March 17

OP
It would help if you tell us the date you are traveling

I'm trying to explain that if I wanted to go from Monopoli to Salerno with only 1 change, the Bologna route would be the only - absurd - option.
This is because The direct Frecciarossa #8302 you are talking about, the train that departs from Monopoli at 7:05 and calls at Caserta at 10:50, is available on trenitalia.com only from March 9 to March 19. I have no idea of the reason, but you can check by yourself.

So the only sensible option to get from Monopoli to Salerno with only one change is the train&bus combo via Bari.