The verb burst is usually uninflected in the past tense and as a past participle Bursted is an old form that still appears colloquially, but it is widely considered incorrect and is best avoided in formal writing. It always bears replacement with the uninflected burst.
Though considered incorrect, bursted has a long history. The Oxford English Dictionary has examples from as long ago as the early 16th century,1 and a historical ngram graphing the use of bursted over the centuries shows that it has never been absent from the language in modern use.2 It is only due to convention (and consensus among usage authorities) that the word is now considered incorrect. And while the form is rare in edited writing from this century, it is fairly common in informal writing.
Here are a few examples of burst used in the past tense and as a participle:
A water main burst in a Friendship Heights shopping district Friday, opening up a gaping hole that almost swallowed a car. [WTOP.com]
Three men burst into the home on 47th Street north of University Avenue about 12:40 p.m. [Sign On San Diego]
Scottish Water said that while problems with burst pipes had yet to materialise, it was prepared for the predicted increase in calls. [BBC News UK]
Bursted appears occasionally, especially in the U.S.—for example:
Even though Castro bursted onto the scene as a 20-year-old, he immediately became one of the best shortstops in baseball. [Daily Illini]
Lubin was sitting in a loan committee meeting, and the chairman of the board bursted in. [Buffalo Grove Countryside]
Saturday Night Live bursted out of the gate last night with a very strong cold open on the Vice Presidential debate. [Gothamist]