Sonny Bono's political aspirations are swelling. Cher's ex-husband, now the mayor of Palm Springs, Calif., says he is thinking about running for the Senate in 1992. "I will begin researching what it will take to win the election and making myself aware of the issues that most concern the people of California," Bono, a Republican, said. "Recent events in California . . . have convinced me that the time is right for me to explore the feasibility of my seeking election in 1992. As a successful songwriter, singer, restaurateur, businessman and now, mayor, I have always tried to learn from my various successes and failures. I have shared the American dream and participated in the challenges that face every businessman and family in this great state."