Information
In the episode "Weirdmageddon 3: Take Back the Falls ", Bill Cipher travels into the mind of Stanley Pines (cleverly disguised as Stanford) in order to find the equation that is needed to escape the town. When he enters to room to find Stanley, Stanford (in the real world) begins to erase his mind using the gun first introduced in the episode "Society of the Blind Eye ". As he does, the room goes up in flames; blue flames to be exact (this is important because it the the color of flames when Bill makes a deal). Slowly, he is engulfed in the flames and takes many different forms as he is meeting his untimely demise. He speaks in a backwards message as he plunges further into madness before finally being defeated by a punch to the eye delivered by Stanley.
There is much speculation as to what Bill Cipher is saying, but the most common iteration is as follows:
A-X-O-L-O-T-L, my time has come to burn! I invoke the ancient power that I may return!
Meaning
Ever since this aired, loyal GF theorists have rushed to analyze this from start to finish, trying to figure out what Bill is saying as he dies. Some believe instead of saying A-X-O-L-O-T-L, Bill is instead screaming the A out in agony as he dies, followed by spelling out X-O-L-O-T-L.
Xolotl is an Aztec deity often associated with: underworld, misfortune, sickness and twins.
An axolotl is often referred to as a "water salamander", and is a rare creature known for being able to regrow its body parts.
He could be calling out to the deity of the underworld as he collapses, also because a central theme of the show is the bond between twin siblings. Or, since we see Bill regrowing his eye (twice actually), it could be a reference to him acting like an axolotl and regenerating after his demise. And, A-X-O-L-O-T-L is the keyword used to solve the cipher on the bus seat near the end of the episode, so it is most likely that he is spelling out axolotl.
Along with this, there is an analysis of the rest of it too. Some people believe him saying "I may return" is a nod from Alex that A) Bill could return to Gravity Falls B) Gravity Falls itself could make a comeback, or C) there could be a spin-off involving Bill. It could also just be a “you haven’t seen the last of me!” exclamation that villains often shout as they’re dying. But, coming from the show where one of the main symbols (the cipher wheel) is an archaic prophecy, ancient powers might not be something to just shake off.