The timeline of events in The Empire Strikes Back is left unclear by the film itself, so how much time actually passes in the Star Wars movie? After the action-packed Battle of Hoth opening, the Rebel heroes each go their separate ways. Luke Skywalker and R2-D2 head to Dagobah for Luke’s Jedi training, while Han, Leia, Chewbacca, and C-3PO desperately trying to evade the Imperial fleet. The Empire Strikes Back switches between the two storylines, but doesn't explain when they're happening in relation to one another. How long was Luke’s training on Dagobah? How many days were Han and Leia on the run from Darth Vader before he intercepted them on Bespin?
In most cases, non-movie material from the current Star Wars canon and original Expanded Universe (aka Legends) clears up questions like these without any ambiguity. Unfortunately, the amount of time that passes in The Empire Strikes Back is one of the few exceptions. No complete timeframe has been established for the film in the current canon, but one can be extrapolated through various sources. Legends, however, does definitively explain the amount of time that passes in the film.
The most helpful resource in determining The Empire Strikes Back’s timeline is the Legends-era book Star Wars: The Essential Atlas. This guide states the exact years, months, and days of the movie’s first and final scenes, according to the Galactic Standard Calendar and Great ReSynchronization notation system. The first scene in The Empire Strikes Back takes place on 38:6:6 (the sixth day of the sixth month of 3 ABY), and the film ends on 38:7:7, meaning that in the Expanded Universe, The Empire Strikes Back takes place over the course of exactly a month.
With the Legends timeframe in mind, it isn’t unreasonable to assume that the same amount of time passes in the current canon’s version of The Empire Strikes Back. Without a guidebook to directly give the dates, one must look to other sources. The most direct reference to a timeframe in canon comes from the anthology book From a Certain Point of View: The Empire Strikes Back. In Obi-Wan’s story, he describes Luke’s Jedi training as having lasted only a few weeks. According to specifications found in Star Wars: Millennium Falcon Deluxe Book and Model Set, the Millennium Falcon’s life support and consumable supply could last up to two months, which would allow Han and Leia’s plotline to fit within this timeframe as well.
Considering how much growth the characters of The Empire Strikes Back go through over the course of the movie, this timeframe makes sense. For Han and Leia, their affection for each other grows significantly between their time on Hoth and arrival on Bespin, more than it could have in a matter of days. In Luke’s case, his tutelage may have been brief, but it allowed him to hold his own against the more experienced Darth Vader for a short time. Yoda’s training also taught Luke enough of the basics that he could finish his path to Jedi Knighthood on his own before facing Vader again.