Bishop is a powerful man, controlling one of the two most powerful families in the city (the Mordinos are arguably just as influential, since they corner the Jet market). He is seeking to end New Reno's mob-based anarchy by bringing it into an alliance with the NCR and Vault City. As part of this process he is working within the NCR's congressional system to legalize prostitution and gambling within the Republic. The NCR hired Bishop as a middleman, who in turn hired the raiders who harass Vault City, in the hopes that Vault City will turn to the NCR for protection.
He is a neglectful husband, indifferent to the fidelity of his wife Leslie Anne Bishop, and he cheats whenever it suits him. He has also provided little guidance for his daughter, Angela Bishop, who like her mother is promiscuous and also a Jet addict. Nevertheless, he is extremely possessive and easily incited when one impinges on his perceived territory. Bishop once skinned a boy whom he found out had gotten his daughter drunk.
If the player has sex with Angela Bishop or Mrs. Bishop, if the player speaks to Mr. Bishop and refuses to take a quest for him, he will threaten them to do the job or pay for their actions. Continued refusal, or visiting him again without completing the quest, will turn Bishop hostile.
The player can kill Bishop discreetly by changing the combination to his safe, thereby killing him with his own booby-trap. To do this, sleep with Mrs. Bishop, and afterwards suggest killing her husband by way of an "accident" (this option only appears if the Trap skill is at 76%). The player can then go to Bishop's safe and use Repair on it to change the combination. The player can then leave and return later to find Bishop dead. If the player set off the trap on Bishop's safe themselves, they will have to "use" plastic explosives or TNT on it to re-arm the trap before using Repair to change the combination.