It takes about four minutes to bleed out from a severed femoral artery.
I imagine a jugular vein would be about the same.
Plenty of time to put a full magazine of 45 ACP into his torso, at contact distance so no misses, reload, and put 8 more rounds right into his heart.
Then sit down and light a last cigarette.

Of course, to let a man with his hand in his pocket get that close without drawing your gun is bad tactics.