Rental Car Drop Off Choices

I need to know the exact address of you apartment in Florence to give you the best advice.

We will be walking distance from SMN train station. Thx

That doesn't tell me much. The entire historical center is walking distance from the station. I need to know the exact street to know if you can even drive to your apartment. Most of Florence city center is not accessible to motor vehicles without a special residents' permit.

Address is Via Faenza 8. Thanks.

Your apartment is not accessible by car, it's in a pedestrian zone. These are your options.
Park at a local garage. Just blocks away from it there are however a few garages that you could access, such as:
http://www.giglioparcheggifirenze.it/
http://www.parkopedia.it/parcheggi/garage/garage_nazionale_di_carfora_luigi/50123/firenze/
in addition to the larger Underground garage at the station or even the Central Market garage (expensive though)
To reach them however you have to be careful and make sure you notify the garage so that they can enter your vehicle in the City website "White List". However I could give you directions on how to reach them without stumbling in any ZTL cameras.
Although you said that the extra days will not cost you any additional charges, however, those garages will charge you for parking. You won't need the car at all during your stay in Florence and the car will stay parked the whole time. The rates are over €25/day ($35/day).
So you need to weigh in your costs and decide.
If you keep the car you will incur parking costs of over €25/day. In addition the 70 mile trip to Bologna will cost you approximately €25 in gas and tolls.
If you return your car in Florence, you will save the parking costs and the hassle of driving in Florence (and to Bologna). However you will incur train fare costs from Florence to Bologna. The cost of one way train ticket to Bologna on Standard class is €24 p.p.. However if you pre-purchase in advance online on www.trenitalia.com you might be able to secure tickets at discounted price (at €13 or €15 per person). Just make sure that you make that specific train you book, because discounted tickets are not refundable.
The train option is hassle free and much faster than the car. By car the trip from FI to BO is approx. 1.5 hours assuming regular traffic. The high speed train travels in a tunnel under the mountains at 300km/h and covers the 70 miles from Station to Station in 35 min. If you secure 4 discounted tickets, the train option is not only faster but also probably cheaper than the car option, because 2 days of parking + driving costs to Bologna will amount to at least €80, which is more than 4 train tickets at €15 each.
Even if you decide not to pre-pay online and buy the tickets on the spot, the train costs are €24x4 people=€96. Therefore not much more than the car costs for 2 days and a lot less hassle.
If that were my trip, I'd return the car in Florence or even in Orvieto, if you don't intend to visit anything between Orvieto and Florence.
If you intend to visit some little towns or the countryside of Tuscany on the way between Orvieto and Florence, then you should keep the car after Orvieto, drive through Tuscany all the way to Florence and return it as soon as you hit Florence. Then go to your apartment, by taxi or walk (the rental car offices are on Borgo Ognissanti, which is walking distance to your apartment). Then you would take the train to Bologna.

Car rental prices are cheapest when you book for a whole week (5, 6, or 7 days may all cost the same), but there should also be reasonable prices for 3- or 4-day rentals, if that's enough time to cover most of what you wanted to see around Orvieto. Try Auto Europe among your car rental quote options.

Roberto, a million thanks for your detailed explanation of my options! We will definitely not bother with keeping the car in Firenze so now just need to decide whether to drop off in Orvieto or Firenze. Laura, thanks as well..