NeverarGreat’s headcanon is reasonable. I think the official explanation is that the Falcon (and most ships) had a backup hyperdrive, designed only to get you (slowly) to an inhabited system for repairs.
My preferred explanation is that it’s a fairly dense area of space, such that systems are closer together than in our region, and that it still probably took several months to get to Bespin. This, of course, aligns with Luke needing more than a few days’ training with Yoda.