Kombucha culture (named SCOBY-Symbiotic Culture of Bacteria and Yeasts) and milk kefir grains represent multiple consortia of wild microorganisms that include lactic acid bacteria, acetic acid bacteria and yeasts with valuable functional properties. Their fermentative potential provides a wide range of derivate metabiotics (prebiotics, probiotics, postbiotics and paraprobiotics) with valuable in vitro and in vivo benefits. This study targeted the evaluation of the functionality of a co-culture of SCOBY-based membranes and milk kefir grains, used as freeze-dried starter cultures, for the fermentation of a newly formulated medium based on black tea infusion, supplemented with bovine colostrum and sugar, in order to produce bioactive compounds with functional properties. The design and optimization of the biotechnological process were achieved by using the Plackett–Burman experimental design (six factorial points, three center points) and the response surface methodology and central composite design (three factorial points, six axial points and two center points in axial) tools. The statistical analysis and the mathematical modelling of the responses such as the pH, titratable acidity, antioxidant activity and antimicrobial activity (against Bacillus subtilis, Escherichia coli, Staphylococcus aureus and Aspergillus niger) were investigated. Further, the composition of organic acids, polyphenols and flavonoids of the fermented product obtained under the optimized fermentation conditions was also analyzed. The fermentation of the medium containing 6.27% (w/v) bovine colostrum powder, 1.64% (w/v) black tea, 7.5% (w/w) sugar, pH 6.7, with an inoculum based of 0.36% (w/v) milk kefir grains powder and 0.5% (w/v) SCOBY-based membrane (both as freeze-dried culture), at 30 °C, for 5 days, in an aerobic stationary system, revealed an antifungal activity between 80 and 100% against Aspergillus niger, an antibacterial activity of 8–22 mm against Escherichia coli and Bacillus spp. And a titratable acidity of 445 °Th. The chemical composition of the obtained product had a positive impact on the functional properties of the fermented products in terms of the antimicrobial and antioxidant properties.