Time to Walk from Ponte Vecchio to Basilica San Miniato al Monte?

Regarding the time of Vespers at San Miniato al Monte, do check the website shortly before you leave. My memory is that the time of Vespers changes by an hour, depending on the season. It's also an absolutely stunning church; I think it's one of the prettiest in Italy. So I'd suggest giving yourself an hour or so to explore the church before Vespers. (I believe you can visit after Vespers, but the extra light of an earlier visit would be helpful.) And do bring coins to light the apse mosaic and the ceiling of the sacristy. The church is fairly dark, and it's well worth turning on the lighting. Finally, sunset is stunning from the plaza outside the church; I like it better than P Michelangelo (although I've always taken the bus back down the hill after dark).

If you're fit it's about a 30-minute walk, part of which involves steps. Bus route #12 goes to Piazzale Michelangelo. Some people take the bus up and walk down. Below is a link to a neat little walking tour with a bit of description; it's a less-direct route than is possible, but it adds interest. Yes, there is Gregorian chanting, but it was at 5:30 PM when I was there, so check on that. It's one of the things I long to return to Florence for. There's a difference between hearing Gregorian Chant in a performance setting vs. in situ as part of the daily liturgical ritual of a monastic community. Deeply inspiring and uplifting. http://travel.nationalgeographic.com/travel/city-guides/florence-walking-tour-1/

We took the bus up there, so cannot give you a good estimate, but did walk down and it took about 25 minutes. I Google mapped it, and it states that it is 1.6 km and approximately a 23 minute walk. Piazza Michelangelo would be on your way down/up, so you would pass it on the way to the church. I guess the amount of additional time depends on how much time you would want to linger there.

We took a very nice route up through the Giardino Bardini, rather than costa San Georgio as shown on that map Rose linked. We exited at the top by the Forte de Belvedere, and then followed the route from there. There were wonderful views over Florence from various places in the gardens, as good or better than the view from Piazzale Michaelangelo, and without all the traffic. But you would have to pay the admission fee for Giardino Bardini. It was a combined ticket with Boboli Gardens so we went there afterwards, but they may not still be open if you get there in the evening ( after vespers at San Miniato).