Introduction: The pressure of the COVID-19 pandemic on healthcare systems led to limited roles of infectious diseases services, increased rates of irrational use of antimicrobials, and incidence of infections by multidrug-resistant microorganisms. The aim of the present study is to evaluate the incidence of antimicrobial resistance and the management of bloodstream infections before and during the COVID-19 pandemic at the University General Hospital of Alexandroupolis (Greece). Materials and Methods: This is a retrospective study conducted from January 2018 to December 2022. Data were collected from the University Microbiology Laboratory per semester regarding the isolated strains of Gram-positive and -negative bacteria in blood cultures and respiratory samples in hospitalized patients in medical and surgical wards and in the intensive care unit (ICU). Additionally, bloodstream infections with requested infectious disease consultations were reported (n = 400), determining whether these were carried out via telephone contact or at the patient’s bedside. Demographic data, comorbidities, focus of infection, antimicrobial regimen, duration of treatment, length of hospitalization, and clinical outcome were analyzed. Results: A total of 4569 strains of Gram-positive and -negative bacteria were isolated. An increasing trend was reported compared to the pre-pandemic period in the incidence of resistant Gram-negative bacteria, particularly in ICUs. Prior antimicrobial use and the rate of hospital-acquired infections were increased significantly during the pandemic. In the pre-pandemic period 2018–2019, a total of 246 infectious disease consultations were carried out, while during the period 2020–2022, the number was 154, with the percentage of telephone consultations 15% and 76%, respectively. Detection of the source of infection and timely administration of appropriate antimicrobial agents were more frequently recorded before the pandemic, and 28-day mortality was significantly reduced in cases with bedside consultations. Conclusion: The empowering of infectious disease surveillance programs and committees, rational use of antimicrobials agents, and bedside infectious disease consultations are vital in order to reduce the impact of infections caused by multidrug-resistant strains.