Contact; The Bellagio. They offer Limo service from the Airport to the Hotel.
There are too many limo companies in Las Vegas. You could try limozu, and they will search all limo services in the area for the best price. Many of the companies offer Airport tranfer at real low price, and the limo service will take care you from A to Z just like a Super Star.
You can have a sedan pick you up at the airport for about 35 dollars you just need to reserve this service from any limo company in Vegas before hand. A cab ride will set you back about ten bucks to the strip. Most limos are about 75 bucks an hour.