Hi Carl,
On Friday, I just returned from a two-week stay in Rome. I was there the same time last year and took note in the increase of travelers and the like. The weather was at least 15-20 degrees warmer during the day than last year. Some other variables probably factored into the visitor increase too. Even the desk managers and restaurant agreed.
I would walk to most places, but I did take the autobus on occasion (1,50 €) per 100 minute (validated) ride. I noticed the buses were not as frequent, or they were very full. But I had no real issues or fear riding them in the early/late evening. I usually would catch one to return to the area of Termini where my hotel was. You can purchase BIT tickets for (autobus and metro) at Tabacchi or some gift shops.) It may be good to keep one or two extra in your money belt. They don't expire until you validate the first ride - either bus or metro. I think the ticket is good for one metro ride. I may be wrong. But, the autobus, once you validate your ticket, the ride is good for 100 minutes including a transfer.
This year, I saw an increase of the Inspectors getting on the buses at random and inspecting tickets/passes They can/will fine you on the spot if your ticket is not validated or expired. One bus I got on had an "invalid" (non valido) machine to stamp ticket. Other riders had the same issues. In that case, you write the time you got on the bus, the stop you got on, day and bus number - #64 - Bus "3657" for example. You can locate the number of the bus on the outside (back) of the bus if you don't see it near the driver.
The Inspector told me this is okay because some machines are not working all the time. Also, take a picture of the invalid stamp machine to further protect yourself. Oh, and, if one stamp machine is not working, try another in the bus - there are two. That is, if you can get to it. The information on how to proceed (from the Inspector) should suffice.
This year, I took the metro (one time.) I was further out of the city centre. Last year, I did not take the metro. So, I have nothing to compare it too with this year's experience.
The metro car was not too full at the stop I got on. But, the people traffic did increase as we moved on to other stops (going toward Termini.) The metro station is like most big city train stations - be prepared for craziness, "underground" scents that are not pleasant, maybe a person or two asking for money, and people running this way and that way. There are police there at the turnstyles. Getting off and walking out is a bit of a walk; but not that bad.
Keep nothing in your pockets - not even in zippered pockets - jackets or pants. Put all valuables in a money belt under a tight shirt. If you are using some type of security bag, keep that directly in front of you - with a hand on it just for good measure.
If you practice common sense and an awareness/sense of security, you will be fine. If a person has a pre-planned mindset to steal, and an opportunity arises, they could act on it.
The train ride is not scary really. I'm used to people jamming onto buses and onto trains. But, if you choose to not get on one that is already crowded, just wait - another one will be on its way within minutes. The buses were fine as I stated above.
Be prepared. Keep calm. Keep your wits/awareness. You should be fine if you need/want to ride the buses or metro. Many drivers, Inspectors and Police speak English if your Italian is not at "conversation level." They know travelers can be nervous. Side note: Bus #40 at Termini is an express bus - fewer stops, fewer people. Keep the route in mind for certain attractions.
Edited. Guess I'm still on Roma time ;)