CHEATS
Back in the days of the first generation of games (Red, Blue, and Yellow), people used to come up with all kinds of crazy "cheats" -- things they claimed were secrets in the games. (Think Missingno, only more absurd.) There were cheats that covered pretty much every aspect of the games to the point where if you can think of it, it was probably a part of a cheat at one point or another.
The same holds true for Bill, who had the misfortune of having a minor graphical glitch behind his house. Namely, behind the Sea Cottage where there should have been a solid, rock wall was a line of pixels that made it look like the space behind the house actually led up to a warp, or a doorway to another area.
Naturally, the fanbase at the time jumped on it and created two very similar cheats: Bill's Secret Garden and Bill's Mountain.
Both cheats start off the same. You need to catch all 150 Pokémon (barring Mew) and defeat the Elite Four. After that, you need to set your party in a certain order. Here's where the cheats diverge for essentially the only time (besides, of course, the description of the location behind the Sea Cottage). For Bill's Mountain, the typical layout is Dratini, Dragonair, Dragonite, Articuno, Zapdos, and Moltres (in this order). For Bill's Secret Garden, the order is Eevee, Flareon, Jolteon, Vaporeon, and, for whatever reason, two Geodude.
Either way, the format of your team is very specific. Once it's set, the next step is to speak to Bill. He would tell the player that he's very impressed by the full Pokédex and give the character a key to his backyard. Using the key, the player can then access the space behind the house and walk northward until they hit the warp to get to the next area. There, they will either find a mountain (area covered in ledges with patches of grass here and there) or a garden (abundance of grass) where they'll be able to find extremely rare Pokémon like Mew.
Like many other cheats back in those days, these never worked, either. However, the fact that so many people talked about it most likely eventually led to the "path" being filled in from the GSC games onward.