The bus from the airport is a huge impovement over the train. It was more money but it was well worth it.You can take an airport bus directly to Cannes fron the Nice Airport although the price was about a little steep(about 12 euro) .It took us straight to Cannes with minimal stops.
It's much better than the train which costs about 5 euro and you need to take the bus to the station also the tickets will take you about an hour of standing in line.
Bus 600 and 610 go half hourly to Grasse, takes about 50 minutes, starts at the Gare Routiere on the eastside of the train station.
Bus 200 via Antibes to Nice, 2 to 4 per hour, 1.5 hours (much longer in heavy trafic), starts west of the trainstation next to Monoprix department store.