The race track is up in the hills a bit above Fuengirola. As far as I know there is no bus service there but the train from Benalmadena will take you to Fuengirola and there is a taxi rank there. I have not seen any adverts for a special bus service up there but maybe some of the local bars in Benalmadena will be organising something, worth checking it out when you are here.

there is a bus service from Benalmadena to Mijas. It runs up through Arroyo de la Miel. Check it out at Torremolinos bus station. There is also a frequent bus from Fuengirola to Mijas.
web.com/benalmadena/html/benalmadena_bus_timetables
Have a look at this site.

Be aware the Hipodromo is nowhere near Mijas (not unless you are a jet-propelled seagull). It is just a mile or so north of La Cala. Bus to La Cala from Fuengirola, then a taxi, seems the best solution.

TA78, it may seem like that from La Cala but it is closer to Fuengirola especially if you are travelling from Benalmadena. Taking the bus from Fuengirola to La Cala and getting a taxi will take longer and there are far more taxis in Fuengirola than La Cala.

The link below is from the racecourses own site.

http://www.hipodromocostadelsol.es/pages/situation.php