Accents
Accents say a lot about a character because, even if the stereotypes are cringe-worthy, the way a person speaks just gifts them with all the connotations associated with their dialects. In other words, we still judge them based on how they speak, even if we don't mean to. This is especially true in Pokémon, where chances are, if a character has a certain accent, they also have the personality traits that go with them.
Bill just so happens to use three distinct dialects, which means all kinds of fun things for him.
Osakan
Canon: All Japanese
In every single form of Pokémon media in which Masaki pops up (yes, even the anime), he speaks using Osaka-ben, a dialect specific to the city of Osaka, Japan. (Because Goldenrod City is the Pokémon world's equivalent to Osaka, this makes a lot of sense. What doesn't is the fact that Bill and Whitney seem to be the only characters who use Osaka-ben, but that's Pokémon for you.) Thanks to the Japanese perception of Osaka, the dialect is considered to be a laid-back way of speaking. That is, characters who use Osaka-ben are usually down-to-earth, impatient, relaxed, loud, the comic relief, the kinds of people who hit first and ask questions later, and all kinds of other stereotypes you might associate with Southerners or New Yorkers (the two most common dialects that Osaka-ben is translated into).
What does this say about Masaki? Depends on the canon. In Electric Tale of Pikachu, he's not the comic relief until his second appearance, where he takes on the sillier aspects of the dialect's associations. On the other hand, because the entire chapter is rather silly in general, this personality change isn't necessarily because of his dialect. Likewise, in the anime, he's a completely serious character all around (although Team Rocket are, unbeknownst to him, making puns at his expense throughout the episode), the dialect is actually rather ironic.
As for the games and Special, he's generally seen as the universe's butt monkey, so the dialect has some effect on his character. This goes especially for Special, where not only has he been known to do things like run off onto a ledge of a window during Red's battle against Deoxys, but he's also been seen as loud, obnoxious, or otherwise worthy of being blown off by the other characters. All around, he sports a relaxed personality (compared to, say, the anime) and has been known to be pretty open with both his emotions and his opinions. In other words, the dialect definitely fits him.
Southern
Canon: Special
In Special, Bill's use of Osaka-ben has been translated into a thick Appalachian accent. This particular dialect is usually associated with a lot of the same things as Osaka-ben: someone who's laid-back, loud, very open with their opinions, and prone to being the comic relief. On top of that, the accent also implies a lot about the character's education; the Appalachian (or any Southern) dialect is usually given to unintelligent characters.
As stated above, a lot of the traits of the dialect still fit Bill, but the uneducated part serves as a spike of extra comedy. Specifically, Bill is simultaneously the smartest character and the least informed: while he holds a lot more credentials than a number of characters and knows more about Pokémon and science than most of the cast, he also can't battle and can't keep himself out of trouble, the two most vital skills in the entire series. That, combined with the other perceptions of the accent, pretty much cement his status as the comic relief.
(Of course, it's also amazingly ironic, too.)
English
Canon: Anime
For whatever reason (my guess is probably due to his attire), Bill's Osaka-ben was translated into Queen's English in the anime. Not sure what Queen's English is? It's the accent most Americans think of when they imagine someone speaking with an English accent. (It's also called King's English, Oxford English, BBC English, or Received Pronunciation.) To an American (like the ones who produced the Pokémon dub), the accent has pretty specific connotations. Characters who use it are usually perceived as being educated, posh, reserved, extremely polite, and possibly stuffy, to name a few adjectives.
Considering how serious Bill's character is throughout his episode (even during times that were actually more comical in the original Japanese), this might make a lot of sense. Bill was meant to be portrayed as both extremely intelligent and upper-class, and as such, the anime simply went with the accent that portrayed that the most easily. Or, in blunter terms, the anime loves stereotypes more than any other incarnation of the Pokémon franchise. So, Bill's a walking stereotype too.
Most other versions of the translation don't make Bill's dialect particularly clear. While he speaks in a relaxed manner, this is only as direct a translation of the original Japanese as one can get; there's no indication that he's speaking with any particular accent beyond that.