Wesley was the son of Wesley Sr and Margaret Fischer Bishop who were married about 1917. They were also the parents of a daughter, Sarah Elizabeth Bishop.

Wesley Jr graduated from Moorestown public schools in June 1939. He enlisted in the US Naval Reserves (NSN:405-09-03) V3 program on 14 Oct 1940 in Camden, NJ. He received his radioman training at the Naval Radioman School in Noroton Heights, CT. He graduated from that school on 5 Mar 1941. He was detached from Noroton and transferred to the Receiving Ship, San Diego, CA. via commercial carrier. He arrived in San Diego on 08 Mar 1941. From San Diego Bishop was transported to Hawaii on board the troop transport USS Wharton (AP-7). He embarked on the Wharton on 20 Mar 1941 in San Diego. While at sea, he became ill. After disembarking from the Wharton on 03 April 1941, Bishop was hospitalized in the US Naval Hospital, Pearl Harbor for about three weeks.

After being released from the hospital, he reported on board the battleship USS Arizona (BB-39) for duty later in April. On the evening of 06 Dec 1941 Petty Officer Bishop left the ship on liberty to have dinner with friends in Honolulu. He had planned to remain ashore until Sunday. However, he was unable to find lodging in town so he returned to the ship. Early the next morning, the Japanese attacked Pearl Harbor and the Arizona. Most of the crew died in action including Petty Officer Bishop. He was first reported missing in action on 20 Dec 1941. Confirmation of his death came a month later via telegram from the Navy Department that he had been killed in action on 07 Dec 1941. He became the first WWII casualty from Moorestown, NJ. On Memorial Day 1998 a new recreational complex in Moorestown was named in his honor.