score:4
You may have to change buses once or twice. After all, these are in two different countries. The website you cite has connections between Torres del Paine and Puerto Natales as well as Puerto Natales and El Calafate in Argentina. Buses between El Calafate and El Chalten in the Los Glaciares park are frequent.
However, you can get more direct transportation via the small tourist agencies you find everywhere in these towns. Especially in El Calafate I saw many of them advertising tours to Los Glaciares and Torres del Paine, as well as packages including both. Since (judging from your other question) you'll be flying out of El Calafate, it makes sense to have that as your "base camp" and make multi-day trips from there to El Chalten and Torres del Paine.
Keep in mind: this is South America. They don't have everything organized perfectly, but they make up for it in flexibility. If you have multiple people wanting to make a specific trip for which there is no official bus schedule, they'll just find some guy with a minibus to take you there.
Some more advice (I just travelled the region using a rental car in November):