Valencia Airport to Javea by Bus
There is only one practical bus service from Valencia airport to Javea, Beniconnect only offer private taxi services, but national carrier Alsa does offer a service without having to change buses in Valencia City making it more convenient the equivalent Alsa service from Alicante airport.
There is an issue however, in that there are limited journeys, often only one or two buses per day, in addition these buses are offered at different times on different dates, so you will need to check the Alsa site to see if it corresponds with your flight.
Journey times run around three and a half hours and drop off passengers at the bus station in Javea. The bus station is some distance from the beach and many accommodation areas around town, but there is a taxi rank at the bus station, there is also a cafe.
Alsa will allow small pets and other items such as bicycles to travel with you on the bus, the cost at the time of writing (Winter 2016) is €15.55.
It would be possible to take a bus or taxi into Valencia City and then catch a bus to Javea, but unless you have no other choice the journey would be very long and inconvenient. There are no train services between Valencia City and Javea or Denia.