Summary
Bradley had an opportunity to show that he could be a solid backup center during the '19-'20 season with the Jazz, and failed t provide that level of play. The Jazz were much worse with Gobert off the floor (which, to be fair, has continued since Bradley's departure as well, although not to the same extent), and overall didn't trust Bradley with playoff minutes. The Jazz gave away picks just to move Bradley and get enough room under the hard cap to replace him with Derrick Favors, who they later also had to sacrifice a pick for in order to move him.

Bradley had a decent season in Oklahoma City in '20-'21, and while he still only got a minimum contract in 2021 with Chicago, he at least got a player option for the second year. Bradley has shot well at the rim for the majority of his career, as his eFG% was near the top of the league from 2019-2021, but that has dipped down to just slightly above-average in '21-'22.

Overall, Bradley was unable to make any impact on the Bulls, playing in under 500 minutes of non-garbage time, according to Cleaning the Glass, and having his spot as the backup center taken by Tristan Thompson after the Bulls acquired Thompson in February.

Bradley has decent hands and works hard on the glass, especially on the offensive glass, as his offense rebounding rate is near the top of the league. However, Bradley isn't athletic enough to be much of a lob threat, and doesn't have the range to stretch the floor at all either. It's hard to be a productive center in today's NBA without either of those skills.

On defense, Bradley can use his size to protect the rim, but he's slow-footed and will get cooked if he has to try and defend on the perimeter at all. Bradley is still only 24, so we could see some improvement, particularly in just overall defensive awareness and positioning, but I don't think Bradley is much more than a third center whose value is a minimum contract.
 
Cap Considerations
Bradley has a $2 million player option for next season, and if he declines that option he will be an unrestricted free agent with a $1.7 million cap hold and Non-Bird Rights. Due to the increase in the salary cap, his minimum salary for '22-'23 is about $70k more than his player option amount, so he should opt out as long as he believes he can get a fully-guaranteed minimum contract.

If Bradley opts for free agency, the Bulls will be somewhat limited in their means of re-signing him. Since they will only have his Non-Bird Rights, the most they could offer him using the Non-Bird Exception is a contract starting at $2.5 million. The Bulls will likely have either the $10.3 Non-Taxpayer Mid-Level Exception or the $6.3 million Taxpayer Mid-Level Exception available to re-sign Bradley if $2.5 million isn't enough.

Other teams will have multiple ways to sign Bradley as even teams without cap space could possibly use any of the Non-Taxpayer MLE, Taxpayer MLE, or possibly even the Room MLE or Bi-Annual Exception to sign him. Since he signed a minimum contract in 2021, teams will hope to get him at the minimum in 2022 too.