Are their buses that travel from SAN Airport to Sun City,Ca?

No there are none. Public transportation from San Diego to Riverside county is practically non existent. You need a car to do anything in So Cal.

If you can't rent a car, your only real other option is Greyhound.

It's actually easier to get there from LA than San Diego.

They run private shuttle buses out of LAX or O/C, but none out of San Diego.

In any case it's going to take hours and be expensive. It actually might be cheaper renting a limo for half the day.

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LMAO not unless you maybe count greyhound