Budew can be caught early in Pokémon Brilliant Diamond and Brilliant Pearl, but evolution takes a lot of work. Like Budew, there are a number of Pokémon in Shining Diamond and Shining Pearl that require high friendship to evolve. If that's not enough, Budew requires another parameter: you have to evolve it with high friendship throughout the day.
In Shining Diamond and Shining Pearl, "day" means 10:00 to 19:59 in your local time. Thankfully, this means that the twilight hours of the game also count as "day" for those of us who like to play in the evening. Unfortunately, getting Budew to evolve at the right time is the easy part.
Maybe not all Budews are as picky as mine (which eventually evolved to the mature level of 32), but you'll need to cultivate a high level of friendship with your Budew before it evolves. The best ways to do this are to keep your Budew at your party, feed him the kind of Poffin he likes, go for walks with him, give him the Bell, and let the lady in Veilstone City give him a massage.
If your Budew is like mine, it will resolutely refuse to evolve until it shows two hearts in the Pokétch friendship check. If you're struggling, go to Dr. Footstep's house on Route 213, just southeast of Pastoria City - he'll tell you exactly what your Pokémon needs to feel happier.