In a promotional article published by Gamefan magazine, the game's art style was stated to have been heavily influenced by the Road Runner and Wile E. Coyote Looney Tunes shorts directed by Warner Bros. animator Chuck Jones. On top of this, he was credited in promotional materials for overseeing some of the game's art direction and for choosing the game's flat-shaded, polygonal graphics, but was not credited in the final product.

In the opening title card to the game's penultimate level "Escape from WooL.A.", Bubsy appears dressed as Snake Plissken, the protagonist of the action movies "Escape from New York" and "Escape from L.A.", the latter film of which the level is named after. Beyond that, inputting the password "XURASNAKER" on the Load/Save menu will allow you to play as Bubsy while wearing the costume in any level.

Bubsy exhibits some rather unique idle animations, including changing TV picture settings and other cut-scenes that show him juggling and performing various acts.

The European version of this game has no memory card support. A password system replaces the load function seen in the North American version.

Originally a Sega Saturn port of the game was planned to be made, as seen in promotional material from Winter 1996. This version was most likely cancelled because of the poor reception and sales for the game.

All of the characters in the game were voiced by the same actress, Lani Minella.

Bubsy 3D contains an unused copyright screen for a Japanese release, licensed to Coconuts Japan.

The US box art of Bubsy 3D contains quotes from a review by PSExtreme magazine claiming the game to have received a "Gold X Award". For many years, the combination of the magazine's obscurity and the generally-accepted notion of the title's low quality led many to believe that the quotes and award were faked.

This was disproven in 2018 when Redditor Alex Winding provided a scan of the magazine to Retrovolve writer Josh Wirtanen.

While Bubsy 3D is often considered to have killed the Bubsy franchise until its revival in the late 2010s, the franchise was not killed by Accolade as one may expect. Accolade wanted a new installment titled Bubsy 4 (Bubsy in Fractured Furry Tales not being considered part of the franchise's official numbering) after Bubsy 3D's release, but series creator Michael Berlyn was the one who pulled the plug on the franchise, believing that Bubsy 2 and Bubsy 3D had dealt too much damage to it:

Bubsy voice actress Lani Minella had concerns that Bubsy was too annoying during recording, but her voice directors simply told her that this was by intent.

There is an unused death cutscene in the files of Bubsy 3D of Bubsy falling through a floor. This may have been an animation for falling through pits, or suggest that fall-damage was at one point going to return as a mechanic from Bubsy in Claws Encounters of the Furred Kind.

The root of Bubsy 3D's disc contains a copy of the ending cutscene for the level "Escape from WooL.A." titled "DUMMY1.DAT". This file, and two additional copies of it named "DUMMY2.DAT" and "DUMMY3.DAT", are also present in the original US release of Syphon Filter.