Bore diameter is .224", shoot .224" bullets. Winchester 22 Hornets made before WW2 had .223" bores, but since WW2 22-cal centerfires have been pretty much standardized to .224" (other than the 22 Jet and 22 Hi Power).
Before WW-II all Hornets were 223. After the war they were manufactured in 224. The interesting thing is you can shoot 224 bullets in a 223 gun without damaging it.