ZODIAC
Blood Type O
In Japan, blood type means more than just who you can donate to. Rather, the Japanese view it on the same level as how some westerners view their zodiac sign. It says a lot about a person's personality, habits, even what kinds of relationships they'd be able to form.
Bill's blood type, according to Special, is O. Type O people are typically outgoing, loyal, and friendly, the kinds of people who display confidence in spades. On projects, they're initiators. With their abundance of energy, ambition, and flexibility, they're the kind of people who know how to get things started. However, they can also be fairly flaky: although they might start projects and although they're passionate about what they do, they don't always finish them successfully.
How This Relates to Bill: Well, on the positive side, he's got the passionate, energetic, and friendly part down. Not so much with the part about the inability to finish what he starts, though. If his track record has anything to say about it, he's actually more or less the opposite of a type O in that regard. Except for Special, at least, considering it took him an entire arc of putting off fixing the Storage System to finally figure out what was wrong with it. (He also has a temptation to run off to where the action is in the FRLG arc before he reminds himself that he has work to do -- probably an instance where traits of his blood type were offset by traits of his zodiac sign.)
Capricorn
Also according to Special, Bill's birthday is December 31, which plants him smack in the middle of the timeframe assigned to the Western zodiac sign, Capricorn the Goat (date range December 22 to January 19).
As a cardinal earth sign, the first words that pop into one's mind when thinking about a Capricorn would probably be things like "traditional," "hard-working," "practical," "responsible," and "independent." On the downside, the other words that pop into mind would probably be things like "stubborn," "pessimistic," "miserly," "distrustful," and "unforgiving." Whoops.
In all seriousness, Capricorns are typically sensible people. They're patient, steadfast, and ambitious, and to make things even better, they can couple this with their resourcefulness, organization, and love for efficiency and prior planning. In other words, if you want to get anything done, ask a Capricorn. It's probably better if you did: Cappies are also known as extremely reliable, the kinds of people who keep to their word.
As for relationships, Capricorns tend to be extremely loyal, and they're known for putting their family and friends (and, for that matter, work) before themselves. However, be warned! Capricorns set high standards for themselves, and they expect others to be doing the same. If you're not, prepare to face a Capricorn's highly critical side. Moreover, just because a Capricorn is loyal doesn't necessarily mean they'll trust you. As one of the most independent signs of the zodiac, Capricorns hold the philosophy of "if you want anything to get done, do it yourself." They'll usually shoulder their work and baggage on their own, rather than trust anyone else to do it for them.
Also, don't be surprised if it's a little difficult to communicate with a Capricorn. Goat people are also often considered more serious (and more uptight) than people born under any other sign because they're so focused on their own goals and maintaining a sense of order with everything around them. However, one shouldn't be intimidated by them, either. Underneath that aloof exterior tends to lie an insecure goat just looking for stability and security. Once you understand that, getting along with a Capricorn should be easy, provided you make it clear you won't get in their way. After all, Capricorns are stubborn in a lot of ways, including where their loyalties lie.
How This Relates to Bill: It's hard to say. With Special (where the date originated in the first place), it's easy to see his stubbornness with how frequently he has to be forced to do things he doesn't want to do, even if it's for the greater good. (For example, when Blue needed to see Red's data to locate him in the Yellow arc.) Likewise, it's fairly clear that he's loyal to Red (cheering him on whenever possible), although the trainer certainly came across Bill's unreasonably critical side when they first met. Bill has also been known to have an untrusting side when Blue realizes he locks his door at night (despite living in the middle of the wilderness) and during his inner monologue in subsequent chapters about whether or not he should trust Blue at all. At the same time, as I've mentioned under blood types, he also has a slightly flighty attitude that comes to light in either his temptation to abandon his work or his occasional procrastination tendencies. (Although in his defense, the things he was attempting to do instead turned out to be more important than actually fixing the Storage System... despite the fact that the latter was what he was ordered to do repeatedly by the Fan Club President.)
How it fits otherwise depends on other incarnations. For example, it fits the anime's Bill to a T. Overwhelming amounts of patience (to the point where he vows to wait at his lighthouse for a Pokémon that might not appear again)? Check. Distrustful nature (i.e., living in the middle of the wilderness in a lighthouse whose doors have no knobs)? Check. Independence? Check. Seriousness? Check. Maybe even a little stuffiness, too, depending on viewers' opinions. In the meantime, Electric Tale portrays a more amiable, easy-going, and open-minded Bill. Likewise, the games show him getting along well with Celio (as in, no critical nature), trusting the player character to help him out, and generally being a little more relaxed than a typical Capricorn. However, if there's one thing both of these last two incarnations have in common, it's the fact that ultimately, they're reliable and incredibly down-to-earth. (Unless, of course, we're looking at the next-to-last chapter of Electric Tale, but still.)