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Long-distance buses connect Puno to La Paz, some of them are really comfortable (buses from Peru are generally better than Bolivian ones).
There are two things you can't miss when connecting those cities, so I'd recommend you make at least one stop in the middle. There are plenty of connecting buses, so it shouldn't be a problem.
Copacabana is one of the main Bolivian towns on the shore of Lake Titicaca. The main square and the Church are beautiful, and the town has a nice range of hotels and restaurants (try the fish soup and the fried fish, both usually made with fish from Lake Titicaca).
If you can get there in the afternoon, you can climb to El Calvario (a small hill very close to the city center) to see the sunset over the lake from there. It's an unbelievable view.
The second thing you have to see is Tiwanaku, a pre-columbian archaological site and one of the most important precursor to the Inca Empire. It was the ritual and administrative capital of a major state power for approximately five hundred years.
It's only 72 km from La Paz, and there are tours and buses that take you from La Paz to Tiwanaku and back during the day. Also, if you enjoy archaeology, during the summer you can probably see people excavating in the area.