The upgrade "OG Coyote Time" allows Bubsy to walk on air temporarily when walking off of platforms, with the description quipping "looking down optional". This acts as a reference to Looney Tunes character Wile E. Coyote and a recurring physics gag in classic cartoons where characters can walk on thin air off a cliff and only start falling after noticing they are not on solid ground. However, the upgrade has a double meaning; "Coyote Time" is a game development term named after the character and this gag, referring to an invisible mercy mechanic that gives a very short window of time (roughly a tenth of a second) for a platforming character to jump or walk back before falling down a pit.

Bubsy's more mature personality and shirtless jacket outfit featured in Bubsy 4D led to some furry fans developing a renewed interest in the character as a sex symbol. Lead developer Fabraz welcomed this after the game's reveal and retweeted a selection of safe-for-work fanart, social media content and fanmail that spawned from this response. He would eventually reveal that before settling on a tie to use as Bubsy's modern equivalent to the exclamation point on his old shirt, they were going to give him a collar, remarking following the game's reveal: "I don't think the internet could have handled this one."

Oblivia, a character who originally appeared in the Bubsy cartoon pilot, makes her first video game appearance in Bubsy 4D with a redesigned appearance, which most notably gave her a hearing aid. According to lead developer Fabraz, this change was made as a callback to the pilot, where Oblivia was depicted as having bad hearing. Additionally, while the pilot saw her mispronounce Bubsy's name on accident, she was changed in Bubsy 4D to mispronounce it on purpose to amuse herself.

Arnold the Armadillo, Bubsy's sidekick in previous games, does not appear in Bubsy 4D outside of a cameo appearance in a photo. When asked about his absence, lead developer Fabraz stated that he was "on a journey of self-discovery doing a road trip across the country with his new truck", suggesting that the character had overcome his longtime fear of trucks that was established in his first appearance in the Bubsy cartoon pilot.