First you must take a flight from Buenos Aires to El Calafate. There are about 16 daily flights from Buenos Aires to El Calafate in high season.
Then, you can take the bus from El Calafate to Puerto Natales, there are about 2 Regular line Buses, its about 350 km and the trip takes 4,5 hours including the border documentation.
The next day or if you arrive early, you have to take the Bus from Puerto Natales to Torres del Paine.
IMPORTANT: Due to bus schedules from El Calafate, is probable you won’t be able to connect the same day to Torres del Paine, you must consider doing it the next day. We suggest you to ask in the different Bus companies.