In early August, I will be traveling solo for 5 days between a birthday celebration in Monte Argentario and a wedding in Greve in Chianti and before the first location had been chosen decided to see Matera and some of Puglia. It is a logistical nightmare to get south from the first location and also I do not want to rent a car. From what I've read, it's not ideal to see Puglia without a car, but would appreciate any thoughts on how I can make this work.

So my questions - I have one day for Matera, coming from Bari, any suggestions on an economical way to get to Matera and maybe stop off in Altamura on the way? My hotel will pick me up for 100 euro but I don't want to spend that much if there are alternatives. I then will need to get to Lecce and not sure what options there are (bus, train, hitchhike?). I'm staying in Lecce for 2.5 days and would like to do a trip down the coast but would happily settle for checking out the Grotta della Poesia and Otranto, which I think I can get to via bus or train but not sure if this is doable. Otherwise I will have a few days in Lecce but seems a shame not to see more of the area and the coast. I inquired with some Puglia tour companies about driver and guide for day trip but it's off the charts expensive for one person. What is the best way to get a taste of this beautiful area in the short time I have with no car?

My last day will be Saturday in Lecce, then traveling to Bari (bus, train) by evening so I can catch a morning train to Florence. Any thoughts or recommendations are much appreciated.

I visited the area by public transportation and was happy with my experience!

You can take either a bus or train between Bari and Matera; I don't know about stopping in Altamura. You can also go from Matera to Lecce by bus or I think I went by train, but I routed through Bari because that's the order that worked for me.

Consult rome2rio.com and be sure to check through the links to which it sends you, as the main site is not sensitive to seasonal variation in schedules.

Hope that helps!

as kja says rome2rio is the place to start
a longer distance bus in Italy is called a Pullman and surfing on that will help

Thanks kja and Bill, I've seen that come up in my searches but wasn't sure how reliable it is. I'm glad to hear it is doable without renting a car.

I don't know if you've already looked into it, but you can take the train from Lecce to Rome, then connect to Florence, rather than going back to Bari from Lecce to catch a train to Florence.

Don't trust R2R but click through and read the details behind which may resolve issues to do with festivals etc.
Airports are especially well connected.
Train system in the area is based on two structures, the wide lines and the narrow gauge the second of which is great fun to use.

the 'private' (not really but not part of Trenitalia the State Railway system) narrow-gauge (tracks closer together - trains smaller) is yes fun to use but may not appear in Trenitalia data base (or may?) - but no need to pre-book anything on it - dirt-cheap.