There are buses from Alicante airport to Alicante (frequent) and buses from Alicante to Almoradi (less frequent). This may be a bit of a detour and I would check schedules carefuilly before committing (check the Alicante to Orihuels bus, this passes through Almoradi). I don' think there is a more drect connection by public transport. Especially if you are on a late arrival, this might be an iffy option.
If you're feeling a bit more adventurous, another option might be the train to Callosa de Segura and a taxi from there. the best way to do this would be to catch the C6 bus from the airport, get off at San Gabriel Estacion de Cercanias and catch the train to Callosa de Segura from there. This is the Murcia service. It is more or less hourly on weekdays. If you're traveling light you can also walk from the airport to Torrellano and catch the same train there.
In view of your late arrival, maybe a limousine transfer wopuld be the safest option
http://www.shuttledirect.com/
This message was last edited by amogles on 21/04/2015.
This message was last edited by amogles on 21/04/2015.