FAMECHECKER
The Fame Checker is an FrLg-only device given to the player by his or her rival just before hitting the Nugget Bridge. It was basically a feature in the game that allowed players to collect facts about each of the most important characters in the game in order to get bits of backstory and learn a little more about the Pokémon world than had been previously possible in the games. Each character got six quotes scattered throughout the game (including from signs and bookshelves) that went towards unlocking a secret seventh quote from the characters themselves.
For this game series, Bill was actually considered to be one of the NPCs important enough to have his own page in the Fame Checker, but luckily, many of his quotes are pretty easy to find. Consider this a very short guide on who to talk to in order to get Bill's page completed.
First Quote
Source: Your rival, just after defeating him near Nugget Bridge.
Type: What does this person do?
Quote: "After all, BILL's world-famous as a POKéMANIAC. He invented the POKéMON Storage System on PC, too."
Second Quote
Source: Little boy with a hat in Cerulean City's Pokémon Center.
Type: Favorite kind of POKéMON?
Quote: "BILL has lots of POKéMON! He collects rare ones, too!"
Third Quote
Source: His grandfather in Fuchsia City (closest house to the gym, by the bookcase).
Type: What is this person like?
Quote: "He's my grandson! He always liked collecting things, even as a child!"
Fourth Quote
Source: Celio, One Island's Pokémon Center. (Random quote. Keep talking to him to get all three.)
Type: Favorite kind of POKéMON?
Quote: "BILL is a POKéMANIAC, so he loves every kind. Apparently, the first one he caught was an ABRA."
Fifth Quote
Source: Celio, One Island's Pokémon Center. (Random quote. Keep talking to him to get all three.)
Type: Family and friends?
Quote: "BILL's hometown is GOLDENROD CITY, where his folks still live. I've heard that it's quite the festive, bustling city."
Sixth Quote
Source: Celio, One Island's Pokémon Center. (Random quote. Keep talking to him to get all three.)
Type: There's a rumor...
Quote: "Apparently, BILL simply can't stomach milk at all."
Final Quote
From: BILL
To: PLAYER
Hey, there! CELIO had nothing but praise for you. Hearing that makes me happy. When you catch some rare POKéMON, come show me, okay? Promise!