how was the “bleeding kansas” resolved?
a constitution was written for a slave state.
the fighting ended but the problem was not resolved.
the territory became a free state.
it was not resolved until the civil war.

Kansas entering the Union as a free state ended the violence because there was no more argument about the status of slavery: 

Following the passage of the Kansas-Nebraska Act in 1854, thousands of Northerners and Southerners came to the newly created Kansas Territory. Some of these settlers simply wanted the new land now open to settlement, but many other people came to cast their votes either for or against slavery. The Kansas-Nebraska Act had allowed the people residing in the Kansas Territory to decide for themselves whether or not to permit slavery. Some Southerners hoped to make Kansas a slave state, hoping to reduce the North's advantage in the United States Senate. Many Northerners intended to prevent slavery at all costs. Three distinct political groups occupied Kansas: pro-slavers, free-staters and abolitionists. Violence broke out immediately between these opposing factions and continued until 1861 when Kansas entered the Union as a free state on January 29th.