Ciao ParDu,
Don't worry - it is your time and your itinerary, you can surely follow the plan you've set - I'm not saying your itinerary isn't possible to do, that is surely not my intention. Since you asked for help in figuring out whether the bus would be the best way to see the city, I am also trying to bring to your attention factors you should consider for the plan you have in mind. I am also assuming this is the first time you're in Italy and that it is likely you don't/can't come back in the near future which is the reason you're trying to see as much as you can in the limited time you have.
From my own personal experience, when I first came to Italy distance between each of the cities seemed so short compared to distances back home (California). But I quickly realized that in Italy relatively small spaces hold treasures every where you look. So seeing everything from a bus might just give you a "blur" of what is out there and you'll end up seeing general views of what is out there but seeing very little in the end.
Try to imagine this: ride past the Colosseum in Rome in a bus, then actually walking by it, standing right below. The Roman Forum is right next to it but you won't be able to see it from the bus, since it is only open to pedestrians. You can ride around the Vatican but walking into the center of St. Peters Square can only be done on foot, regardless if you decide to go into St. Peter's or not. The size, shape and beauty of the monuments themselves, even if you aren't an art lover or history fanatic will be part of the experience that Italy offers.
The same goes for Florence - the historical center is practically off limits to buses since the area between the Duomo and Via Tornabuoni became closed to traffic. The bus used to pass right in front of the cathedral, now you can't do it. Now it goes around the center, never into it.
In Venice, you can go down the Grand Canal and admire the beauty of the city and its many palaces but the most beautiful of all, St. Marks Square, requires you to walk into it. I definitely recommend you don't miss going into this cathedral or the wonder of its small narrow streets that can quickly make you get lost.
All of this takes time so what I was proposing earlier is to spend a day in Rome, sleep there, then head to Florence, spend the day there, sleep in Florence then head on to Venice (save over an hour getting there), enjoy the city, sleep in Venice and then return to Rome. Of course, if your itinerary permits you to get back to Rome in time for your departure. Given the limited time you have in each place, saving 2-3 hours of travel back to Rome means you have 2-3 more hours to savor each location. Each of these cities is magnificent at sunset and once the sun goes down all the monuments are lit up. Even if you're not interested in night life, being out and about once it gets dark is beautiful.
You'll see the Tuscan countryside from the train as you travel from Rome to Florence. But if you're in Florence, you could do a 12 hour tour of Tuscany such as this one (
Tuscany in One Day Sightseeing Tour) because it starts in Florence. Look into it, you might be able to get it in and is definitely worth it!
There are public bathrooms but they aren't everywhere.... the easiest is just to head into a coffee shop, buy something, anything and ask to use the restroom (many are reserved for patrons so by buying something you gain the right to use it). In any case, this
map with the public restrooms in Florence should be helpful when you're here
.
I am sure whatever you end up doing in your 3 days, you'll love what you do see of Italy and will somehow you'll make it possible to come back again to spend a little more time in each place
