Caesar had no bodyguards. In fact, Appian says that he bluntly refused to re-enlist his veterans as a bodyguard and appeared in public accompanied only by his magisterial retinue (μετὰ τῆς δημοσίας ὑπηρεσίας ἐπεφαίνετο μόνης--ὑπηρέτης literally means "rower," but it's used as a synonym for Latin apparitor, the low-level public servants like lictors and scribes who accompanied magistrates everywhere). All of our sources tell the same story in different terms. Both Plutarch and Appian say that when a bodyguard was offered him, either from his Iberian veterans (Appian) or his personal friends (Plutarch), he refused and said that it was shameful to be always fearing death. Cassius Dio (always a troublesome source) says that he was granted a bodyguard of equites and senators, which is to say that the entire body of the senate and the equites were supposed to protect him, and that he dismissed his bodyguards because he had no fear that those very people who had proposed his honors would ever do something to him. Suetonius offers up the possibility that Caesar refused to enlist his veterans as bodyguards either because he wanted to expose himself to the plotters or that he wanted to show publicly that doing him in would be worse for the state than leaving him be--I think Suetonius' first suggestion, that Caesar simply trusted the oaths of the senate, is easily the most plausible, although having armed bodyguards within the city was also decidedly un-Roman