"Soon afterward"
Luke intends in his gospel to present events in order (Luke 1:3). This episode is the next thing Jesus did after the woman washed His feet while He ate at the house of Simon the Pharisee.
Thus, Luke emphasizes that Jesus, for His part, responded to the previous episode by preaching and evangelizing through both city and countryside.
The Pharisee's attitude toward the formerly sinful woman—he would not even allow her to touch him—would also have impacted his own teaching; he certainly spent no time teaching among the common people far and wide.
The Women
Luke tells us many women serve the Lord and His workers by providing for their day-to-day needs, like food and lodging. They are doing an important work, participating in the spread of the Gospel. God certainly provided a reward for them.
Despite the women's notable devotion and service—in some instances, they stood by the Lord closer than the apostles did—the apostles do not esteem the women as they should. For example, the women are the first to learn of Jesus's resurrection, but their report is not believed.
Luke 24:10–11…these words seemed to them an idle tale, and they did not believe them.
Although we may have different roles according to our gender (or age, or position in life, etc.), all souls are of equal value before God! Our prayers to God can be hindered if we do not recognize this Scriptural truth.
Galatians 3:27–29For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus. And if you are Christ’s, then you are Abraham’s offspring, heirs according to promise.
1 Peter 3:7Husbands, live with your wives in an understanding way, showing honor to the woman as the weaker vessel, since they are heirs with you of the grace of life, so that your prayers may not be hindered.