maybe a taxi once you're in Siena is the best solution...
Ciao Stuart,
You're very welcome! I understand your confusion with the bus schedules, didn't realize how they were set up until now that you point them out. Didn't realize everything is on one single .pdf - yikes! Let' see if I can help you make some sense of it all...
In terms of a PORTA or entrance through the walls, the address you cited is closest to
Porta Camollia.
I don't know the bus routes in Siena so I've plugged in the address you gave on Google maps and zoomed in to see where the bus icons pop up. I clicked on the two nearest ones and see the list of bus lines passing through the stops called "Piazza Chigi Mercatino" and "Via Campansi".
Then referring back to the Siena bus website, I found a map of the lines here:
http://www.sienamobilita.it/mappe/Mappa_URB.pdf
The train station is the one to the left of CENTRO marked as "Stazione F.S." - your direction is toward Centro by heading to Piazza del Sale.
Your stop will be before this. From the station, you have several choices of bus lines - the 3, 10 or 13.
So all the timetables on one single .pdf here -
http://www.trainspa.it/train04/urbano_si.pdf
On page 11 you find the times for the first line, the 3. The "A" after the bus number means "andata" or going and the "R" means "ritorno" or return....
the two little hammers crossing like an X at the top of the columns mean work days which is Monday-Saturday, the cross is for Sundays and holidays.
You find the stop "Siena V.Campansi" before "Siena FS" (the train station) so it means this is for buses traveling in the opposite direction you're interested in. So skip to page 14 to start seeing the times for the bus in the right direction.
Since "Siena FS" is the train station, the next stops are on Via Mazzini and then on Via Garibadi -- since it is a different route, this makes it likely that Via Campansi is a one way street even if Google maps doesn't mark it as so... and given this, it seems that the closest bus stop for your location will actually be Piazza del Sale.
If you map this on Google, you can see where it is in relation to your address. I don't think it is very far considering how small Siena is and, if I remember correctly, this is relatively flat area so you could just walk to your address from there. But if you feel you have too much weight with the suitcases, I actually suggest you consider just taking a taxi from the train station.... the ride will be pretty short directly, whereas the bus will drop you off still some distance away. The express SITA bus from Florence drops you off in Via Tozzi near the stadium which is closer to Piazza del Campo but further away from your address.
Hope I haven't given you too much information and confused you - but after looking everything up, it seemed better to just share everything as well as my final recommendation
(8 days in Florence sound wonderful - you'll feel like a native by the time you leave

- if you get the hang of how the buses and trains work in those days, you'll get to Siena without a problem )