Some straight (i.e. probably filtered through management) dope:

The Bulls never wavered from their stance of not trading reserve big men Omer Asik or Taj Gibson and dangled first-round picks in their talks with teams. They still possess roughly $2.9 million of salary-cap space and will monitor if any possibilities become available via buyout.

Sources said the Bulls offered two first-round picks for Rockets guard Courtney Lee, but that the Rockets insisted on Asik.

The Bulls also engaged in talks with the Grizzlies regarding guard O.J. Mayo, who reportedly was nearly dealt to Indiana for Josh McRoberts and a first-round pick, but the trade fell through at the deadline. But the Grizzlies asked for Gibson and multiple picks, according to a source, and the Bulls had concerns over backcourt size issues with Mayo and Derrick Rose.

Also mentions minor talks regarding Jared Dudley, Anthony Parker, and Corey Brewer.

So this is interesting, and more concrete than 'Bulls should've upgraded!' sentiment. We (sorta) know the cost:

Would you have dealt picks+Asik for Lee?

Would you have dealt picks+Taj for Mayo?

I had a feeling the latter was possible when that now-defunct Mayo to the Pacers deal leaked. I would've done it. If it turns out Mayo wasn't the best fit due to size, then just don't re-sign Mayo in a year. Would've been an interesting potentially high-ceiling move to see Mayo as a 3rd-4th option on this team playing alongside (and what appealed to me, backing up) Derrick Rose.

Taj is fine insurance but he's up for an extension eventually too.

As far as buyouts go, I predict that it'll go like the offseason: players take less money and go to Miami. Though actually, Troy Murphy is reportedly already likely going to Boston.