Nobody protected senators, they were private citizens without legal magistracy and holding only advisory powers. Curule magistrates (consuls, praetors, curule aediles, etc.) and magistrates holding imperium were accompanied by lictors. Lictors weren't really bodyguards, though. The only weapons they carried were the ceremonial stone axes on the fasces, which were removed when within the pomerium anyway, and in the historical period their right to execute had lapsed. Their duties were pretty much totally ceremonial rather than practical: they walked in single file in front of magistrates, announcing his presence and bidding everyone except married women and Vestals to let him pass, and a small subset of the college of lictors assembled the comitia curiata. They formally held rights of arrest and summon, but without much physical ability to carry out these duties by force one wonders how real a power that was on a daily basis, and after magistrates began to be accompanied by viatores this right must've been largely symbolic. The number of lictors also changed depending on the magistracy, and in some cases a sitting magistrate had no lictors at all--since the consuls alternated presiding over the senate and comitia every other month, the twelve consular lictors only accompanied whoever the senior consul was in any particular month, not both. The college of lictors also appears to have provided lictors temporarily to private citizens as well, particularly those holding elaborate games and stuff like that, but this was not a legal responsibility and they cannot have carried fasces during these duties. Rather, this must have been a mark of prestige for the private citizen who hired them out, as no man of any important, sitting magistrate or not, was without an extensive retinue. For sitting magistrates the lictors were only the most conspicuous of these apparitores, the cluster of retainers and aids who accompanied every man of political importance and wealth, magistrate, senator, or not. They were not the most important, though, but somewhere in the middle--the scribae that senators often looked down on ranked higher than lictors.

Like I said, though, important men in Rome were never alone. They were always accompanied by a cluster of hangers-on, both official and hired, and during a politician's morning walk to the forum, for example, by a throng of clients. Only occasionally--after physically stepping into the curia, for example--was a man of any importance actually alone. Still, for some the threat of physical violence was real, and hired bodyguards are known to us. They mostly consist of a couple of strong-arms rather than a whole contingent--often these men are gladiators. Sometimes these armed retinues could be quite large, but it's exceptional. When Milo and Clodius clashed on the Appian Way they were both accompanied by large retinues (Clodius' numbered 30 mounted men) of armed slaves, including at least two gladiators on Milo's side. In this case, however, the large armed bodyguard was the result of the fact that both Milo and Clodius were travelling outside the city, as Asconius mentions (ut illo tempore mos erat iter facientibus, "as it was customary in those days for those travelling to do"). The use of large bodies of soldiers as bodyguards within the city, accompanying an individual at all times, was distinctly un-Roman, and the praetorians didn't really do this during the Principate at all. Caesar, for example, is said by Appian to have refused to call up his Iberian veterans as a bodyguard and instead asked his friends (i.e. his retinue) to watch his person, in good Roman fashion.