bus to Piazzele Michelangelo in Florence

Yes, in the uphill direction, bus 12 comes from the train station and crosses Ponte alla Carraia, so that sounds like your best place to catch it. In the downhill direction, it completes its loop via Ponte San Niccolo. See the map view by clicking the magnifying glass on this ATAF schedule link. Bus 13 follows a pretty much opposite plan, uphill via Ponte San Niccolo and downhill via Ponte Amerigo Vespucci.

From Ponte Vecchio area you might be better using another bus to connect to the #13 bus. On the Oltrarno side, you can catch the D electric bus at the Bardi stop (or the Pitti stop if you're closer to it), get off at the Fornace stop (3 stops - 4 stops if you get on at Pitti), walk about 100 feet (same direction and side of street) and catch the #13 bus at the Ferruccci stop. It's then only 2 stops to Piazzale Michelangelo. It's less convenient from the Ufizzi side of the river, with the best option probably being to catch the #23A or #23B bus at Corso dei Tintori (end of Via dei Neri) and again getting off at the Fornace stop (3 stops). I've used both these options and it's an easy connection. The #12 bus takes a much longer route to Piazzale Michelangelo from the Ponte Vecchio area. If you did want to take the #12 bus, you could catch the D or C3 electric bus at the Ponte Vecchio stop, ride it for 2 stops and then walk the last hundred feet or so to the #12 stop just past the Ponte alla Carraia.

Hope this suggestion isn't too late, but consider just taking a cab. I always find bus routes and schedules to be pretty mystifying. We were at Boboli Gardens in May and took a cab to San Miniato, which is just above Piazzale Michelangelo. It was kinda fun riding along as the driver negotiated the narrow, crowded streets of Florence and up the winding park road to the top of the hill. It was under 20 euros and I practically had to argue with the driver to give him a tip. From San Miniato we walked down to the piazzale and from there back to our hotel a few blocks from the Duomo. Easy and totally stress-free.

It's a nice walk too. Excellent for burning the extra calories ingested in Italy.

I agree with Roberto, the walk is very nice and not very long, about 20 minutes. Just know that it is uphill, but the scenery is beautiful!

If I can tag onto this thread- if we are around the Uffizi and want to catch one of the little trams running along the Lungarno ( to connect with the #12), where could we buy tickets?

CJean, the minibuses and regular buses both use the same tickets. From Rick Steves Florence:

Buy bus tickets at tobacco shops (tabacchi), newsstands, or the ATAF ticket windows inside the train station (€1.20/90 minutes, €4.70/4 tickets, €5/24 hours, €12/3 days, €18/week, day passes aren’t always available in tobacco shops, tel. 800-424-500, www.ataf.net). Be sure to validate your ticket in the machine on board. You can sometimes buy a ticket on board, but you’ll pay more (€2; must have exact change), and you still need to validate it in the machine.

In addition to what Laura wrote, I discovered today (I'm in Florence now), that since July 1st, you can buy by phone SMS text message too. You need to have a local Italian SIM card however (Vodafone, TIM, 3, Wind).
Just send a message to 4880105 and type the text ATAF in the body. Make sure you receive the confirmation text message back before you board, and you basically have a paperless ticket valid for 90 min on any bus. The mobile provider (one the 4 listed above), will deduct 1.50€ from SIM Card credit.

It's a nice walk too. Excellent for burning the extra calories
ingested in Italy.

I'll agree! Exactly what we did!

I also agree it is a nice walk for burning calories! A number of times we have taken the bus up and walked back down. Have also walked up and down and then don't feel guilty having that extra scoop of gelato:)