Besides the flight option mentioned above, you can also contact this company for a private transfer from El Calafate to Puerto Natales. It’s probably pretty expensive, but their bus options are listed as ending at the end of May.
You could also try a taxi company like Remis Condor, but you can see that this is an expensive option.
I think the reason for this is that this is winter time in Patagonia and there are snow and ice everywhere on the roads. It could be really dangerous to drive these road, especially with a bus. You could hire a car in El Calafate or a bigger town, but note, because you are crossing over the Chile/Argentinian borders more than once, the car insurance costs a lot. And obviously you would need snow tyres and snow chains. Your best bet would be to fly to Puerto Natales.