Essential oils derived from plant materials are a mixture of compounds that exhibit antibacterial properties. Due to their distinct aroma, they also serve as a desirable natural additive for various food products, including dairy products. In this study, the essential oils of lemon peels, clove buds, and juniper berries were obtained by steam distillation and characterized using gas chromatography–mass spectrometry to determine their chemical compositions and effects on the viability of seven Bifidobacterium strains. Furthermore, the effect of essential oils on the viability of Bifidobacterium animalis subsp. lactis Bb-12 was investigated in cream samples during fermentation and after storage for 21 days at 6 °C. The fatty acid composition of fat extracted from essential oils containing sour cream samples and the volatile aroma compound profile of the sour cream samples were also determined chromatographically. Among the 120 compounds identified, monoterpene hydrocarbons were dominant in the essential oils of lemon peels (limonene and γ-terpinene) and juniper berries (sabinene and β-myrcene), while eugenol and eugenol acetate were abundant in the essential oil of clove buds. In addition to these compounds, butanoic and acetic acids were found in the tested sour cream samples. In turn, fat extracted from these samples was rich in saturated fatty acids, mainly palmitic acid. Among the tested strains of the genus Bifidobacterium, B. animalis subsp. lactis Bb-12 was the most sensitive to the essential oils of clove and juniper, as indicated by the larger growth inhibition zones. However, both the concentration and type of essential oils used had no effect on the number of cells of this strain present in the cream samples immediately after fermentation and after its 21-day storage, which suggests that the tested essential oils could be a natural additive to dairy products.