The Bucs quickly signed Lawrence Tynes, but he developed a MRSA infection and also missed the 2013 season. Instead, Rian Lindell was the kicker for the 2013 Buccaneers. Lindell was largely average, but missed a few kicks at crucial times. It's no surprise that he won't be brought back.
Lawrence Tynes status with the Bucs is more murky. The Bucs placed Tynes on the non-football injury list in a bid to avoid liability for his injury, but Tynes is still contesting that decision, which cost him an accrued season toward his pension. If Tynes wins that dispute, he will be a free agent, but if he loses, his rights still belong to the Bucs, according to the Tampa Bay Times. I can't imagine they'd welcome him back given the contentious nature of their breakup, but stranger things have happened.
Barth returning does not mean that the kicker will be on the roster for the season. None of his salary is guaranteed, and the team is likely to bring in at least some symbolic competition during the offseason.