(1) Background: Carbapenem-resistant (CR) bacteria pose a significant global public health challenge due to their ability to evade treatment with beta-lactam antibiotics, including carbapenems. This study investigates the biofilm-forming capabilities of CR clinical bacterial isolates and examines the impact of serum on biofilm formation. Additionally, the study evaluates the resistance profiles and genetic markers for carbapenemase production. (2) Methods: Bacterial isolates were collected from the microbiology laboratory of Mures County Clinical Hospital between October 2022 and September 2023. Pharyngeal and rectal swabs were screened for carbapenem-resistant bacteria using selective media. Lower respiratory tract samples were also analyzed for CR Gram-negative bacteria. The isolates were tested for their ability to form biofilms in the presence and absence of fetal bovine serum at 24 and 48 h. Carbapenemase production was detected phenotypically and confirmed via PCR for relevant genes. (3) Results: Out of 846 screened samples, 4.25% from pharyngeal swabs and 6.38% from rectal swabs tested positive for CR bacteria. Acinetobacter baumannii and Klebsiella pneumoniae were the most common species isolated. Biofilm formation varied significantly between clinical isolates and standard strains, with clinical isolates generally showing higher biofilm production. The presence of serum had no significant effect on biofilm formation in Klebsiella spp., but stimulated biofilm formation for Acinetobacter spp. Carbapenemase genes blaKPC, blaOXA-48-like, and blaNDM were detected in various isolates, predominantly in Klebsiella spp., but were not the main determinants of carbapenem resistance, at least in screening isolates. (4) Conclusions: This study highlights the variability in biofilm formation among CR clinical isolates and underscores the differences between the bacteria found as carriage versus infection. Both bacterial species and environmental factors variably influence biofilm formation. These insights are crucial for the development of effective treatment and infection control strategies in clinical settings.