Awful long way to go in just three days, ideally make it four or five. There's three basic ways to do this.
You can contract with a tour company who will take you there and back in a decent vehicle, but of course that will be expensive for a solo visitor.
You can make take public transport (buses and taxis), then when you get to Erg Chebbi make separate arrangements for a bivouac (typically 300-350dh including a camel ride).
Third option is to join a minibus type of tour which consolidates tickets sold by front companies in the side streets around Djemma el Fna. But be aware the transport/service might leave much to be desired. The following link is currently out of action (Lonely Planet is currently down) but gives a flavour: www.lonelyplanet.com/thorntree/thread.jspa…