POKÉMON 101
To get a grasp on Bill's character, it's usually a good idea to start off by asking about his world first. This is in part because he's consciously dedicated his life to the creatures with which he shares it and in part because, let's face it, his world is pretty different from ours.
To make a very long story short, in 1996, Nintendo and a then-practically-unknown gaming company known as Game Freak teamed up to bring one of game designer Satoshi Tajiri's most famous work to the Gameboy: Pokémon Red and Pokémon Green. It began as a simple monster-taming game, wherein a young child left his home in the small town of Pallet to collect and train all of the 151 one mysterious creatures known as Pocket Monsters -- Pokémon for short. The games became a hit shortly afterwards, and it was expanded into four sequels, two reboots, several spinoff games, at least ten seasons of an anime series, several different manga, toy lines, and even a musical production in the United States. Just as the franchise expanded, so did the Pokémon world, introducing new regions and characters and increasing the number of Pokémon in the universe from a mere 151 to, as of this writing, 649.
On a meta-level, a lot of the canon in Pokémon shares the same basic premise. Children at the age of ten leave their homes to go on adventures with their element-bending Pokémon partners. In the course of this, these children make new friends, help their Pokémon grow stronger, and repeatedly save the world from disaster at the hands of multiple evil organizations, all with their Pokémon friends right by their sides. (From there, each canon takes on a different plot. This is just a very general overview.)
Even then, it's hard to say what a Pokémon really is. What's known is this: there are, as of current, 649 different Pokémon species, each one based on a different plant, animal, mythological creature, or even inanimate object. Each one of these creatures possess different powers, including different techniques known as "moves" and different strengths and weaknesses to all of the seventeen known elements (or types) of Pokémon. Considering this, most humans tend to capture Pokémon (via portable devices known as Poké Balls) and use them to fight wild Pokémon or the creatures of another trainer in events known as battles. Some of these trainers, like protagonist Ash Ketchum, go on to compete in regional leagues and tournaments for battling; others, like Ash's friends might compete in contests, breed Pokémon, use them in day-to-day activities, or a number of other possibilities. In short, the relationship between Pokémon and humans runs deep, a lot like the relationship between a dog and its owner.
Despite focusing a lot on them and even forging a society that centers on relationships built with them, Pokémon still largely remain a mystery to the humans of that world. That's where Pokémon researchers like Bill come in. Although Pokémon are magical creatures, they're viewed on the same level as animals or pets to the inhabitants of that world. As such, it's a researcher's job to analyze Pokémon in a scientific light. Some spend their careers carefully cataloguing each new species; others deconstruct Pokémon behaviors and form theories based on observations gleaned through trainers or work on the field. Either way, it's no easy task, and it, like apparently a lot of other Pokémon-related occupations, requires every ounce of a person's dedication.