Hmm...
Spoiler:
This would assume the bottles have caps to keep the water from evaporating, and that he has a compass or other device to navigate in a straight line, or else bad things would happen:
1. He grabs 4 days worth of water, and walks for a day towards his destination. On arrival, he sets up camp.
2. The next day, he leaves two days worth of water at his camp site, and with his remaining day of water he travels back to the oasis where he rests.
3. When he's ready again, he grabs another four days worth of water bottles, and sets out for his campsite a day away. Once there he gets his rest for the night.
4. The next day, he continues walking toward his destination for another day, with his remaining three days worth of water. Once he's walked for another day, he sets up camp again.
5. When he awakes, he heads back to the first camp, after leaving a days supply of water bottles behind at the second camp. Upon arriving back at the first camp, he'll be out of water.
6. After camping at the first camp site again, he then grabs one of the two days worth of water rations and hikes back to the oasis.
7. When he's ready, he grabs another four days of water, and completes his journey to the edge of the desert, replenishing his first day's water at the first camp site, his second day's water at the second campsite, and then having enough water for the remaining four days.
Since I can't think of anything better, I'll just use the example above as the fastest, and assuming he does these hikes daily, it would take 12 days to leave the desert.