As the settlement grew, it was named for a grove of redbud trees which grew there.
Red Bud was chartered in 1867 and the city incorporated in March, 1875.
The city was struck by a tornado on November 18, 1892, which killed two people and seriously injured twelve people.
There were 1,370 households out of which 31.5% had children under the age of 18 living with them, 55.0% were married couples living together, 10.2% had a female householder with no husband present, and 31.7% were non-families. 28.4% of all households were made up of individuals and 16.4% had someone living alone who was 65 years of age or older. The average household size was 2.40 and the average family size was 2.95.
In the city the population was spread out with 23.2% under the age of 18, 8.1% from 18 to 24, 25.9% from 25 to 44, 23.0% from 45 to 64, and 19.9% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 86.4 males. For every 100 females age 18 and over, there were 81.8 males.
The median income for a household in the city was $40,300, and the median income for a family was $50,280. Males had a median income of $36,049 versus $20,957 for females. The per capita income for the city was $19,967. About 6.0% of families and 9.4% of the population were below the poverty line, including 10.1% of those under age 18 and 13.0% of those age 65 or over.