Are there buses or metro connecting LIMA Airport and centro?

I found all posts here are telling us to get a taxi at airport but wonder if they have a bus or metro connecting the centro. I will go to Cruze de Sur's bus terminal at Jiron Quilca 531 to take a night bus for Arequipa. I have plenty of time to kill so would like to take public transportation which seems safer and cheaper than taxi. Any advice?

Thanks in advance