I followed Bobby around for an hour and 20 minutes today. He made it pretty easy for me to do so because he restricted his movements to above the park square, on building perches around the park, and a park tree.
He had to deal with a dive-bombing Peregrine Falcon throughout my visit. The Falcon made a couple of close passes at him when he was on the Judson Memorial Church cross, several dive-bombs when Bobby was perched on NYU's Kimmel Center building, and a couple of dive-bombs when he was flying above the park square.
His day came to a quiet close though and he was able to rest in a tree then disappear deeper into the park trees at roosting time.