Senatores weren't elected, they were chosen by high ranking roman officials. In the early republic this was done by the Praetor Maximus, later by the consul and since the end of the 4th century B.C. by the Censores. They were basically free to choose anyone they deemed fit for the job, but by custom you needed to have held an office of the cursus honorum (the exact requirements changed and were lowered over the years, from only former praetores and consules to even quaestores in the late republic). The censores (or consules/praetores maximi in earlier times) looked into the senatorial lists every five years (after 81 b.C. every year) and added new senators or kicked senators out that broke laws or were seen as to immoral (they could also issue Notae Censoriae, which were basically warnings not to break the customs and laws of the republics, which were seen as extremely humiliating for roman nobles). You could also be added to senate without ever holding senate if you qualified otherwise, e.g. by rendering extraordinary services to the republic.