The Bulls will go into this summer with between 18-21 million dollars in cap space. They will undoubtedly go after one of the top-tier free agents in Dwayne Wade, Chris Bosh, and Lebron James. Many think Wade, and James will likely stay with their current teams. Bosh would certainly be a great signing, but the Bulls will be competing for him against several teams, and it will be tough to get him, and he may decide to stay where he is.
There are still several other very quality options out there in Amare Stoudemire, Carlos Boozer, and Joe Johnson. The Bulls could also add a younger guy like Rudy Gay who isn't quite a top-tier free agent, but would certainly improve the team and most feel he could be signed for between 5-7 million.
I think the bulls could become contenders easily with the signing of Rudy Gay and Joe Johnson. They would need to first move Kirk Hinrich and several teams are interested in him, and could more than likely improve the team, in the long-term also by trading him for draft picks. Joe Johnson would certainly be an upgrade over Hinrich, the bulls would get draft picks for the future and add another young player in Rudy Gay who is averaging 20.1 ppg, and 5.8 rpg this year and is only 23 years old, to the already solid young core of Rose, Noah, and Gibson. The bulls would still have some money left to fill out their roster. I think these moves would definitely be enough for the bulls to make a strong run in the playoffs next year, and put them in line for their next championship.