We sourced these low-profile 18-8 stainless steel screws for your bottle cage to specifically avoid abrasion between the head of the screw and your beautiful Bivo bottle finish. Each packet contains two screws.
They should easily swap out with any bicycle cage. They also will avoid rust, unlike a lot of coated regular steel screws sold with many bikes.
These are M5 x 0.8 mm thread, 16 mm long, 3 mm hex drive, rounded head screws.