So, I did a quick Google and learned that stagecoaches traveled at around 10mph. His wife and son were somewhere in Michigan, to calculate I assumed they caught a ride in Chicago, since it's pretty close to the border of Illinois and Michigan and was the last major metropolitan hub before entering the wilderness of the west. So from Chicago to Deadwood is about 950 miles. So, traveling at full speed, it would be around 95 hours. Since the stage coach seemed small and pretty cramped (it was Bullock's wife, her son, and another woman on one bench and 3 other women on the other and they were all touching. It seemed like the seating was similar to the backseat of a sedan) I assume they took breaks for the night and, possibly meals.
How did that work? Did they all set up tents for the night? Was it one tent per person or did people have to share? If they shared, how'd they deal with the fact that the driver and the guy riding shotgun were both men with a coach full of women? How dangerous was this mode of travel? It seems very dangerous to me, 5 women, a little boy, in the wilderness, protected by just 2 men. Was assault/ rape/ murder/ robbery etc. As common as popular culture makes it out to be, and if so, did people accept the risk simply because it was their only option?
Deadwood was established in the 1870s after the transcontinental railroad was completed in 1869. One would take rail service to Omaha and then a shortline north. In the early days, it would then be necessary to take a stagecoach to reach Deadwood, but the trip would be relatively short.
When longer trips by stage were necessary, there would be stops at "stagestops" - basically small hotels, where passengers could eat and sleep until resuming the journey. Stage drivers were well aware of dangers and well armed to confront any problems. Theft - especially for stages carrying money for whatever reason, was the primary danger.
Edit: typo/date corrected to 1869 (not 1969!) with thanks to /u/filbertsnuts
As u/itsallfolklore says, it'd be a quick ride from the local rail station to Deadwood. If you would like an idea of what a long stagecoach journey was like, one account that's classic- and easy to find- is Mark Twain's of his 1861 staged trip with his brother from St Joseph, MO to Carson City, NV in Roughing It. It was cramped , dusty, and the swaying motion would make people seasick. The food at the stops- what there was- was awful, and there would be places - like where there was deep mud or sand- where the passengers had to get out and walk to lighten the load. Twain and his brother were armed ( with a useless "pepperbox" revolver) , in case of attempted robbery, but there was none. Even Twain's writing can't disguise the fact that it was, really, just a very long, tedious trip.