My idea of the timescales of ESB hinges on the assumption that Bespin is a planet in the Hoth system:
My lord, the fleet has moved out
of light-speed. Com-Scan has
detected an energy field protecting
an area around the sixth planet of
the Hoth system. The field is
strong enough to deflect any
bombardment.
The word ‘system’ in Star Wars can refer to either a planet or an entire solar system. So if this is the case, Bespin wouldn’t be more than a few AU’s away from the Ice Planet of Hoth. Presumably Bespin is closer to the star, past a particularly dense asteroid belt which separates it from the unnamed Ice Planet. It is highly unrealistic for Bespin to be located in another star system entirely, since star systems are usually light years apart. This would require Luke to train on Dagobah for over a year, regardless of the time dilation effects on board the Falcon. Alternatively, if the Falcon traveled at the speed of light across only the Hoth the system, it would probably take less than an hour to make the trip. At even 1/4 the speed of light, this trip wouldn’t need to take more than a day or two.
Of course, this fast travel time implies that either Luke’s training was very brief, or that the Falcon couldn’t accelerate to even a significant fraction of the speed of light. I’d bet on the latter, since the ships in the Star Wars universe act more like they are in an atmosphere than in a vacuum, and thus don’t act as if under constant acceleration with constant thrust. For the purposes of the story, ships have ‘full throttle’ which is their top speed, and even at full throttle the Falcon takes quite a while to make a journey across the Hoth system.
There are several other reasons why the story wouldn’t take months: Vader couldn’t realistically continue a search for that long with so many valuable Imperial resources, rebel forces most likely wouldn’t wait around at the rendezvous point for weeks on end, and it would be highly irresponsible of Luke to abandon his troops for such an extended period of time.
TL;DR: ESB takes place over several weeks at the most, more likely no more than two weeks.