Bus shuttle from Naples Airport to Sorrento

If you have checked luggage, your chances of making the 9AM bus are dictated by the bag reclaim process. In that scenario, I am not betting in your favor.
Not saying it not possible, but its probably safe to expect it will be at least 30 minutes after the plane parks that you will have your bags in your hand, That leaves 20 minutes to get to the bus. Probably enough time IF plane is on time and baggage claim goes smoothly

Your chances are much improved if you can do just carry-on bags.

While Naples Capodicino is a small airport, only 15 gates, you still might be pushing it to get to the Curreri Viaggi bus stop in that short amount of time. There are a few restaurants and several bars plus some shopping areas.

I personally would wait for the 11:00 bus.

Map from terminal 1 to bus area.

http://www.aeroportodinapoli.it/documents/10186/44124/CollegamentiBusGiu2016.jpg/a18714af-aaa9-4388-baf1-114a7447ac6e?t=1484140817000

Another choice would be to take the Alibus, 5€, to Napoli Centrale.
Then take the Circumvesuvian 4,60€ to Sorrento. But the 11:00 bus may beat you there if everything doesn't line up.

Choice 3 would be a private transfer, 90-110€.

Edit to add. Tickets for the bus can be purchased in the arrivals area by the ATM machine.

We did this 2 years ago and didn't pre-book. When our flight landed, I checked at the information desk and they sent us out to the bus area. We were expecting to wait a while for the next bus, but they were just running buses as they filled up, and we paid cash to the driver. It takes longer than they say because of traffic.

The fastest way could be the Alibus to Napoli Garabaldi plaza 5 euros and then to catch the 11:36 Campania Express train to arrive Sorrento 12:30 (it only makes 5-6 stops)