While his esteemed colleagues have valid arguments to win Most Improved Player, I'd like to submit, for your consideration, Patrick Edmunds as the most improved player on the Bulls.
His role hasn't changed...starting SG...and though the Bulls lost a prolific scorer in Andrew Wiggins, our starting lineup remains packed with Van Grimaldi and Alton Hill also getting plenty of touches.
Despite it all, Patrick Edmunds has finally evolved into the leadership role the Bulls envisioned for him upon trading for him.
His minutes have increased from 30.5 -> 33.2. The reason for that? He's fouling a lot less (3.2->2.8) and staying on the floor. He's increased his scoring from 15.6 -> 20.7 points per game, and that's because he's become a much more efficient player (16.2->21.0) who takes better shots and makes more of them (FG% .451 -> .507, 3P% .333 -> .387, TS% .543 -> .600, PPS 1.21 -> 1.32). He more than doubled his EWA (5.8 -> 13.5) in the regular season, but the most important wins yet are the ones he's been getting in the playoffs.
In a 7 game series against his former team, the Oklahoma City Thunder, Patrick led the Bulls in points per game (24.9) while also distributing the ball really well (6.3 APG). Add in a .587 field goal percentage including .483 from beyond the arc, and despite what all the previous stats say, he's the player who's embraced a new key player role most successfully, leading the Bulls deeper into the playoffs.
You can see his player page here:
http://pbsl.ijbl.net/players/player229.htm