Flying was probably the easier option, but I took the bus because it was cheaper (flying was around $200 I recall)
After doing tons of research on this, there seems to be 2 main bus options to get you from Cusco to La Paz
"Regular" tourist bus - leaves from the main bus terminal in Cusco and arrives in La Paz 14 hours later. This is the option I took because it's cheaper and shorter ($20 and 14 hours).
Bolivia Hop - which is a hop on/hop off bus that stops for a few hours in Puno and Copacabana. But you can stop for as many days as you like. You can just catch any one of their daily buses on this route to continue your journey. This option takes minimum 24 hours, leaving Cusco at 10pm and arriving in La Paz at 10pm the next day. Costs $59 USD. You can see details on their official site here. This option is good if you want to check out Puno and Copacabana, which are actually pretty nice because they're both on Lake Titicaca
The regular tourist bus I took was from a company called TiticacaBolivia. They have a listing of all their routes here