The bus network is excellent but this is a 3000+km journey - you'd need to travel from BA to Rio Gallegos with one of the many bus companies, stay overnight then continue onwards to El Calafate with a smaller operator like Chalten Travel.
Use Andesmar.com (when it's working) to find coach routes and prices throughout Argentina - last year it was around $90+$20+hotel. For a long journey the upgrade to Full-Cama is worth every penny, but any of the seats are more comfortable than a plane.
If you're not keen on driving through the wilderness for 3 days consider flying as it's only 3 hours and the price difference minimal if you factor in the hotels. over 7 years ago