I would strongly discourage you from buying him a plastic toy trumpet of any kind. What ya wanna do, to bend this twig, is to make it clear to him–but without nagging or otherwise hammering away at him unmercifully (and ultimately boringly) about it–is that by learning to play this bugle properly, he’s participating in a fine and noble tradition called “Music”, with a capital M. You can phrase it however you want. A plastic toy trumpet will not enable him to participate in a fine and noble tradition called Music, see, because even a Three knows the difference between Real, and Fake, Toy, and Pretend. Encourage him to play his Real Bugle properly, to treat it with respect, to learn to care for it. Get him to play tunes on it–this will tell you if he has a musical ear, because if he can sing a tune, he can pick it out on the bugle eventually. And this is the most fundamental building block of Music with a capital M–being able to sing a tune, in tune.
Also, the plastic toy trumpets I’m familiar with don’t require an embouchure–you just have to blow into them, because they have a fixed reed in the mouthpiece. So they’re really not a brass instrument at all, but a sort of New Year’s noisemaker. So this would be reverse progress, to take him off a Real Bugle and put him on a Bob the Builder plastic toy.
And BTW, start out as you mean to go on and make it clear to him that a Bugle is different from a Trumpet. You don’t have to go into the complex physics reasons why, just point out to him that a Trumpet has keys and valves and is harder to play (perhaps for “Big Boys”?) and plays orchestral and band music, whereas a Bugle is for army calls, like Taps.
And if he seems interested (which however I doubt a Three will have the attention span for, but by the time he’s Five he might), you can explain that a flugelhorn is the band version of the bugle, albeit with keys and valves.
And, er, sorry to rain on yer parade, but he’s not a prodigy. 
As I pointed out, boys have been playing bugles for generations. The toy tin trumpet was a standard toy for boys in the 19th century–there’s one in Tom Sawyer, to signal Robin Hood and his merry men, there in Hannibal, Mo. And babies can learn to whistle. The only thing unusual is that he’s Three.
Just encourage him to keep fooling around with it, explain the idea (with demonstrations) of picking out a tune on it. You want to develop his ear.
Part of the attraction, for him, is that it’s something Grandpa does, too, so it’s a male role model/bonding thing for him. “I wanna be like Grandpa!”, see. If you were into woodworking he’d be fiddling around with your plane.
I would not go whole-hog and enlist a teacher for him, or even present him to some music professional as a prodigy, because, seriously, you’ll just set yourself up for a tactful “Umm…” rejection. Just keep him at it. If he suddenly displays an ability to pick out the theme from the 1812 Overture at a first hearing, then what he needs is not bugle or trumpet lessons, but basic piano, i.e. music lessons. Basic piano will ground him securely in the fundamentals of Music with a capital M, which will stand him in good stead in the future much more than focusing solely on playing a single brass instrument at the age of three.
ETA: I would not allow him to add the bugle to his toy box. You wanna instill respect for it as a Musical Instrument–it’s not a toy, you want to stress. You can let him have custody of it, but IME the more you tell a child he can’t have something, the more he wants it. So if this is a Special Thing that he only encounters at Grandpa’s house, he’s more likely to keep up his interest, rather than have it added to his toy box with all his Star Wars and Legos stuff, where it will blend into the scenery and recede into the background as he moves on to other interests like pirates and dinosaurs.
