A new strain of bacteria producing cellulose was isolated from Kombucha and identified as Komagataeibacter hansenii, named SI1. In static conditions, the strain synthesises bacterial nanocellulose with an improved ability to stretch. In this study, utilisation of various carbon and nitrogen sources and the impact of initial pH was assessed in terms of bacterial nanocellulose yield and properties. K. hansenii SI1 produces cellulose efficiently in glycerol medium at pH 5.0–6.0 with a yield of 3.20–3.60 g/L. Glucose medium led to the synthesis of membrane characterised by a strain of 77%, which is a higher value than in the case of another Komagataeibacter species. Supplementation of medium with vitamin C results in an enhanced porosity and improves the ability of bacterial nanocellulose to stretch (up to 123%). The properties of modified membranes were studied by scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray diffraction and mechanical tests. The results show that bacterial nanocellulose produced in SH medium and vitamin C-supplemented medium has unique properties (porosity, tensile strength and strain) without changing the chemical composition of cellulose. The method of production BNC with altered properties was the issue of Polish patent application no. P.431265.