Saitama seems to have some faith in Bang, as he called Bang to assist him in a competition against Fubuki and her Blizzard Group.
Saitama, while not seeing Bang as a friend and showing disinterest in his martial arts, was still slightly impressed by Bang's abilities from time to time, with the best examples being when Bang defeated him in rock, paper, scissors, and later again when Bang told him how he kicked out Garou after his rampage in Bang's dojo, even admitting that Bang must be "kinda strong". Bang also showed great displeasure when Tanktop Tiger and Tanktop Black Hole were trying to drag Saitama into their "newbie crushing", but didn't interfere, since he had faith in him and even declared him to be the strongest person he has ever met, showing a great amount of respect for the (then) C-Class hero. Bang, realizing Saitama's potential, had since then tried numerous times to recruit him into his dojo, albeit unsuccessfully. He then started to think that Saitama himself must have an incredible teacher too, but when he asked Saitama about it, he was again surprised to hear that Saitama doesn't have a teacher and destroyed the meteor with his strength alone instead of using a technique. He then started to spy on Saitama, and was greatly surprised to find out that he was actually Genos' teacher. Bang was amazed by Saitama's strength and wanted to keep a close eye on Saitama. Saitama first met Bang when the giant meteor was falling towards Z-City. Saitama and Bang playing rock, paper, scissors Saitama also seems to have enough confidence in Genos to handle certain threats alone, as seen when he accepted Genos' request to fight G4 alone without any pressure (although he asked him if he needs help) and would only help/save Genos, when he sees him in need. Despite this, however, Saitama does manage to give Genos some relatively good advice from time to time. Although Saitama has yet to officially call him his disciple (as Genos is always the one identifying himself as his disciple), Saitama actually tries to train him, but since Saitama only knows strength training (which wouldn't help Genos, due to him being a cyborg), most of Saitama's advice/lessons are made up, and only an excuse to keep the cyborg occupied. He is also the person who he spends most of his time with, since Genos moved into Saitama's apartment to live with him. Genos has become Saitama's companion and friend (or at least close to it).
Saitama holds some respect for Genos since he became an S-Class hero right off the bat, and desires to move up the ranks due to his S-Class status. Though Saitama was initially annoyed by the thought of having an apprentice, he gradually warmed up to Genos, even becoming slightly worried and concerned when he saw Genos' limp body after he was defeated by Deep Sea King, or after Genos got smashed into a rock by Tatsumaki.
After being saved, Genos asked Saitama to take him on as a disciple, to which Saitama nonchalantly accepts, thinking that Genos was not being serious. Saitama met Genos after the latter was defeated by a monster and tried to self-destruct, but was instead saved by Saitama.