Here is information for you and more.
1) Alicante Airport (ALC) - Torrevieja bus station (via non-stop Costa Azul QuickAir bus) - Los Alcázares (via Costa Azul Alicante city - Cartagena bus)
2) ALC - Alicante city bus station (via Subus C6 airport bus) - Los Alcázares (via Costa Azul Alicante city - Cartagena bus)
3) ALC - Murcia city bus station (via ALSA non-stop bus) - Los Alcázares (via Lycar bus)
Just choose whichever combination best suits your times...
Links:-
ALC Subus C6 airport bus: aerobusalicante.es/index.php/…
Costa Azul ALC - Torrevieja QuickAir Bus timetable: costazul.net/index.php/en/routes-and-schedul…
Costa Azul Alicante city - Cartagena city (for Torrevieja - Los Alcázares part of journey) timetable: costazul.net/index.php/…alicante-cartagena
Alsa ALC - Murcia city express bus timetable: http://www.alsa.es/en
Enter 'Alicante Airport' as your departure point & 'Murcia' as your destination, enter your travel dates and click on 'Search'.
Lycar bus Murcia city - Los Alcázares timetable: https://www.facebook.com/media/set/…
Bus stops (paradas) where you can get off/board the Costa Azul or Lycar buses in Los Alcázares courtesy of Los Alcázares town council: losalcazares.es/index.php/es/concejalias/55-…
Dunno about 2 bus stations in Torrevieja. Just know of the one in Calle del Mar. Someone else on here or on the Torrie forum may be able to help on that.
You could always ask Costa Azul themselves either via their website linked above (using the 'Your opinion' link on the right of the page) or ask them on their FB page: https:/…201024816642114