The closest you're gonna get to a box set is
The Buddah Box, which covers the label that was home to several of the best-known bubblegum acts. It has representative tracks from Ohio Express, Lemon Pipers, 1910 Fruitgum Company, and Kasenetz-Katz Circus, and marginally bubbly tracks like "The Rapper" and "Brother Louie." But more than half of the box is devoted to other artists on the Buddah label, from Lovin' Spoonful to Gladys Knight to the Fat Boys, and 45 tracks over 3 CDs seems kinda skimpy.
You'd be better served trying to track down the 5 volumes of
Bubblegum Classics issued by Varese. That
25 Greatest... (also issued by Varese) is basically a distillation of the 5 earlier CDs. They average ~20 tracks/CD, but they are OOP and currently fetch silly money on Amazon. You might get lucky on eBay.
Another related series from Varese,
Sunshine Days, compiles more pop nuggets from the mid-60s/early 70s. 5 volumes, lots of HTF nuggets, but also OOP and becoming collectable.
