You may have to change buses once or twice. After all, these are in two different countries. The website you listcite 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, even if there's no official bus schedule.
Some more advice (I just travelled the region using a rental car in November):
- Arrange accomodation in Torres del Paine in advance if you're not camping. It will be expensive.
- Don't make too tight a schedule - leave room for the unexpected. We experienced a fuel shortage in the Argentinian parts caused by strikes and were lucky not to get stranded for a day or two.
- The direct road from Purto Natales to the southern entrance of Torres del Paine at Rio Serrano is being repaired and paved, so this summer the only access is via the much longer road to the north entrance, which is especially annoying if your accomodation is at Rio Serrano