Microbubbles are routinely used ultrasound contrast agents in the clinic. While a soft protein shell is commercially preferable for imaging purposes, a rigid polymer shell demonstrates prolonged agent stability. Hence, combining polymers and proteins in one shell composition can advance microbubble properties. We formulated the hybrid “protein–copolymer” microbubble shell with a complex of bovine serum albumin and an amphiphilic copolymer of N-vinyl-2-pyrrolidone and acrylic acid. The resulting microbubbles demonstrated advanced physicochemical and acoustic properties, preserving in vitro biocompatibility. Adjusting the mass ratio between protein and copolymer allowed fine tuning of the microbubble properties of concentration (by two orders, up to 1010 MBs/mL), mean size (from 0.8 to 5 μm), and shell thickness (from 28 to 50 nm). In addition, the minimum air–liquid surface tension for the “protein–copolymer” solution enabled the highest bubble concentration. At the same time, a higher copolymer amount in the bubble shell increased the bubble size and tuned duration and intensity of the contrast during an ultrasound procedure. Demonstrated results exemplify the potential of the hybrid “protein–polymer” microbubble shell, allowing tailoring of microbubble properties for image-guided applications, combining advances of each material involved in the formulation.