The Bulls currently have the 24th ranked offense in the league (100.9 ORtg). While that might not sound good, they have been climbing steadily up the rankings with a much improved offense as of late. Over the past 6 game winning streak, the team has boasted a 108.8 Offensive Rating, good for 7th-highest in the NBA over that stretch.
It's remarkable that the Bulls' offense has improved so much. Their shot selection is almost the same, as is their free throw rate. Hoiberg has noted that they are moving the ball around more and playing with better pace. It's possible then that the same shots they are taking might be better, more uncontested looks.
Whatever the difference is, the Bulls are making way more of their shots from the same spots as before. This is especially true of their paint shots and midrange shots:
The rim stuff makes sense intuitively - Derrick Rose was awful before on high volume, and now he's pretty good. Noah was one of the worst players in the league at up close shots and he's not in the lineup any more due to injury.
The team has also experienced a bump in its offensive rebounding, which is contributing to better efficiency. Over at DRosesandThorns, Jacob Bikshorn has a deep dive on those numbers:
The surge up the standings is due almost entirely to a huge increase in offensive rebounding. Before December 9th, the Bulls offensive rebound rate was just 22%, 20th in the NBA. Since then, the Bulls have been grabbing 28.2% of offensive rebound chances, the fourth-highest rate in the league.
The boost in rebounding is not necessarily dependent on the presence of the athletic Taj Gibson. Instead, it seems that the Mirotic’s role reduction is the primary cause for rebound success. The Bulls rebound a team worst 47.9% of rebounds with Mirotic on the floor, and just 20.7% of offensive rebound chances.
The lineup changes have had a big effect on the team's play. Hoiberg is continuing to mix and match. He still has a lot of time to experiment and find the right combination and he has a lot of decisions to make.
Now comes the Debbie Downer part: the midrange shooting surge is head-scratching. The team's shooting percentages are way higher than before, and way higher than league average. As good as Pau Gasol has been on those pick and pops, that number is unsustainable - it's going to come down. Maybe not as low as it was before, because the team does seem to be getting better shots in that area, but they're not going to continue to shoot near 50% from long 2.
So there you have it. Better offensive rebounding + improved finishing at the rim + great midrange shooting = a better offense.