Itinerary advice - 13 days for Peru and Bolivia

The Bus from La Paz to Lima is the weak link for me. Take a bus from La Paz to Cusco and use your 2 extra days there. Fly to Lima from Cusco..

Maybe just do a day tour around the Scared valley rather then visit Macchu Pichu on your short timeframe.

agree with #1 - I would also change the part where you fly to uyuni then start salt flats tour the next day to fly to uyuni and start tour the SAME day. If you book in advance agencies will pick you up from the airport.
There is no reason to spend time in Uyuni town..

You could shuffle things around a bit to bus from Puno to Copacabana , spend a day there before going onto La Paz.
You could travel from Uyuni to Potosi instead of coming striaght back to La Paz and spend a day there and do a mine tour.

I agree that you should start the salf flat tour right after you arrive Uyuni from La Paz by air. Take the earliest flight on Amazonas, and you will arrive early morning in Uyuni. My experience is that the guide picked me up at the airport, then sent me somewhere to have breakfast in the town, then tour the town a bit, getting some water...etc, and drove on into the salf flat on the first day. That said, I visited last Christmas, and not yet in the real rainy season. You should allow some time for slower transport during rainy season.

If you have more time, I think you should go further south from the salt flats and into the Dali dessert and the Laguna Verde..etc. Truly amazing landscape and experience.

There isn't much to see in Copacabana, unless you also visit the Isla del Sol. You can easily tour around the church and soak up the atmosphere there while waiting for your boat to Isla del Sol. If you don't want to visit Isla del Sol, then take a short break there for lunch before you move on to Puno. The two places can be visited on the same day, but you will have to stay overnight in Puno if you are travelling from La Paz.

Puno/ Copacabana is at high altitude. You need to acclimatise, and do things slowly. You can take medicines to help speeding up the acclimatisation, but to play safe, I think you should have one more day at the beginning if you fly into Lake Titicaca area straight from a lower altitutde.

I notice that Machu Picchu is not on your list. If you haven't visited it yet, you should go and spend more time there.

With better planning, you can go many places or visit less in a leisure pace in just 13 days.

Enjoy!

I agree with the above regarding Uyuni.

Don't take the bus from La Paz to Lima. It'll easily be 30 hours, if not more. I'd fly again out of Juliaca if you're looking to get right back to Lima. Or, you could also fly to Lima from Cuzco or Arequipa.

I would budget a bit of time to acclimatize to the altitude. A full day at least. Juliaca, Puno and La Paz are all at very high, dizzying altitudes and I'm sure you'll feel exhausted very quickly. It doesn't help that it'll be cold up there too.