None in the B-17. He had been a B-17 Instructor pilot in the US, but his operational missions were in the B-24 Liberator.
Stewart was, as we say in the military aviation community, a stud.
excerpt from his bio.
In August 1943 he was finally assigned to the 445th Bombardment Group at Sioux City AAB, Iowa, first as Operations Officer of the 703rd Bombardment Squadron and then as its commander, at the rank of Captain.
In December, the 445th Bombardment Group flew its B-24 Liberator bombers to RAF Tibenham, England and immediately began combat operations. While flying missions over Germany, Stewart was promoted to Major.
In March 1944, he was transferred as group operations officer to the 453rd Bombardment Group, a new B-24 unit that had been experiencing difficulties.
As a means to inspire his new group, Stewart flew as command pilot in the lead B-24 on numerous missions deep into Nazi-occupied Europe.
These missions went uncounted at Stewart's orders. His "official" total is listed as 20 and is limited to those with the 445th.
In 1944, he twice received the Distinguished Flying Cross for actions in combat and was awarded the Croix de Guerre. He also received the Air Medal with three oak leaf clusters.
In July 1944, after flying 20 combat missions, Stewart was made Chief of Staff of the 2nd Combat Bombardment Wing of the Eighth Air Force. Before the war ended, he was promoted to colonel, one of very few Americans to rise from private to colonel in four years.
In 1966, Brigadier General James Stewart flew as a non-duty observer in a B-52 on a bombing mission during the Vietnam war.
He did appear on the TV series, The World At War to discuss the October 14, 1943, bombing mission to Schweinfurt, which was the center of the German ball bearing manufacturing industry.
This mission is known in USAF history as Black Thursday due to the high casualties it sustained; in total, 60 aircraft were lost out of 291 dispatched, as the raid consisting entirely of B-17s was unescorted all the way to Schweinfurt and back due to the contemporary escort aircraft available lacking the range.
Fittingly, he was identified only as "James Stewart, Squadron Commander" in the documentary.