Is there a direct bus to the airport in Nice?
From where?
The Airport Express bus routes are 98 and 99. They go directly to the terminal with fewer stops. The cost is higher at 6E than the local buses, which also go to the airport area but cost $1.50
I'm planning on walking from Gare de Nice Saint-Augustin. It's about a mile walk (less in a straight line). I realize that's only a reasonable option if you pack very light.
Correcting my typo in my earlier reply: The local buses are E1.50 (and E1 in carnets of 10)
The Train is less expensive than the express bus to Nice Ville but you may still end up with walk or bus/tram to your hotel/apartment at the end. The local routes (Lignes d'Azur) of the buses can sometimes be more convenient -- they don't stop at the terminal like the Express but it's a much shorter walk to the local bus stop (than to the Gare). If you have luggage, Uber is active in Nice and can be quite cost effective for 2 or 3 people (at a significant discount to the taxis).