Bischoff's step brother Blake McLaughlin also plays hockey and was drafted by the Anaheim Ducks in 2018.

[5] He immediately joined the Islanders' AHL affiliate, the Bridgeport Sound Tigers for the remainder of the regular season, posting 3 points in 6 games.

On July 16, 2019, as a restricted free agent, Bischoff was signed to a three-year contract extension with the Golden Knights.

[7] After missing the entirety of the 2021–22 season due to a lower body injury, Bischoff opted to remain within the Golden Knights organization, by signing a one-year AHL contract with affiliate, the Henderson Silver Knights, on July 14, 2022.

[8] Bischoff was later named captain of the Silver Knights on October 12, 2023, succeeding Brayden Pachal.