Bachelet is very popular. Herself.
There is no inmediate reelection in Chile.
The candidate who lost in the second round, Eduardo Frei, was the candidate of "Concertación", the same Socialist-Christian Democrat coalition that led Bachelet into power.
Bachelet (like her predecesor Lagos) is a member of the Socialist party; Frei (like first President from Concertación Aylwin), a Christian Democrat.
Internal bickering within Concertación (and the election of a candidate with little or no charisma) was enough for a soft Chilean turn to the right.