I haven't read Duncan, so I don't quite know what he's talking about. It sounds like something got jumbled somewhere.

Sulla didn't sit outside the city; he entered the city after the Battle of the Colline Gate, herded his prisoners into the Circus, and while they were being executed he addressed the senate in the temple of Bellona. He continued his occupation for some weeks as a proconsul only. Only later did he arrange for the dictatorship.

Appian explains the legal maneuvers. Normally consuls oversaw consular elections, but after the Battle of the Colline Gate, the consul Carbo was still alive. He was not about to hold elections for Sulla's convenience, and was on the run to boot. Eventually Pompey caught and killed him in Sicily.

In that circumstance, the normal procedure according to Appian was that the senate appoint an interrex for five days to hold the elections. Sulla suggested they do this, and when they did he left the city. The interrex Valerius Flaccus, following instructions from Sulla, instead of holding elections for consul, nominated Sulla as dictator and held the election for that.

This was innovative in a couple ways. The interrex had never been used to nominate a dictator before. In the past, consuls nominated dictators after a senatus consultum called for a dictator. Also, it was not a dictatorship with a six month term; it was without term but with a specific brief: legibus faciendis et reipublicae constituendae causa, that is for making laws and establishing the state. You might sometimes see someone claiming this is dictatorship for life; it's not. It has a specific purpose, and presumably when that purpose is accomplished the office expires. In the event, Sulla resigned the dictatorship in less than a year, and possibly around the six month mark.

Sulla certainly didn't wait to enter the city until he got elected dictator, and I don't see any reason to think he paused his activity while searching for an office to give his actions legitimacy. Appian says directly he didn't.