I would argue that the first significant event in this story takes place when Bud makes his escape from the Amos household. Bud, who has been beaten up by an older boy at his foster home, makes his break after being locked in a shed and stung by hornets.

The second main event is Bud meeting Lefty Lewis. Despite being initially terrifying to Bud, Lewis turns out to be a good guy, who gives Bud food and a ride to Grand Rapids, where Bud plans to find Herman E. Calloway, whom he believes to be his father.

Main event number three is Bud's arrival at the club, where he first sees Calloway and makes the bold statement that he is Calloway's son. While Herman wants nothing to do with him, the trumpet player from his band agrees to provide assistance.

The fourth significant event is Bud being accepted into the band members' "family." Having decided that Herman is not exactly the fatherly type, Bud is shown kindness by Eddie and Miss Thomas and experiences happiness for the first time in the story.

The final event that I would put in this list is the roadtrip that Bud takes with Herman when Bud discovers that Herman has rocks with dates and city names, just like the one that Bud has had for years. It is thanks to the rocks that they realize that Herman is probably Bud's grandfather.

This question is open to interpretation, as Bud's journey throughout Bud, Not Buddy has many events.

I would argue that these are the most important events:

1. Bud moves from the "home" to the Amos house

This move kicks off the entire story and gives the reader immense insight into who Bud is and the kind of life he's been living since his mother died.

2. Bud escapes the Amos house

Bud's escape from the Amos house is one of the most dramatic parts of the book. He fights a "vampire," reconnects with his friend Bugs, and even has his first kiss in his escape from the Amos house to Hooverville.

3. Bud meets Lefty Lewis

This is a real development in the story. Other than being dramatic and humorous (Bud also thinks Lefty is a zombie or vampire at first), meeting Lefty gives Bud his first taste of "family" and leads to Bud meeting Herman E. Calloway.

4. Bud meets Herman E. Calloway

This is the moment we've been waiting for since the start of the novel! Bud meets Herman E. Calloway and his band, although Calloway is not exactly what Bud was expecting. We also discover the mystery surrounding the bedroom Calloway is so touchy about...

5. Bud discovers the truth about Herman E. Calloway's identity

Bud finally discovers that Herman E. Calloway is not his father, but his grandfather. Bud receives his saxophone and truly finds his new family, identity, and sense of belonging.

In the book, Bud, Not Buddy, a number of events occur that lead to Bud finding his home and his identity. The first main event occurs after Bud looks in his suitcase at his prized possessions, including a flyer about Herman Calloway and his band. The first event is when he is sent from the Home to the Amos family, where he will be forced to runaway from a mean boy named Todd Amos. This leads to Bud teaming up with Bugs and going to Hooverville. The second event occurs in Hooverville when Bud meets Deza Malone. Deza is Bud's first romantic encounter.

The fact that Bud misses the train leads to the third event, namely, meeting Lefty Lewis. Mr. Lewis drives Bud to Grand Rapids, Michigan, and delivers him to Herman Calloway. Bud mistakenly believes Calloway is his father. The fourth event occurs when Bud is taken to Herman Calloway's house and he sleeps in his mother's bedroom. At this point in time, Bud doesn't have a clue that it is his mother's bedroom.

The fifth, and most important, event occurs when Bud and Herman Calloway discover Bud's true identity. He is Calloway's grandson. Bud also gets his own saxophone and finds his real home and identity.

I would say that the first main event that happens is Bud being moved from the Home to the Amos house.  Bud's done this kind of thing before, and he knows what to expect out of process.  In fact, he nails it right on the head with what to expect out of an older brother.  

Main event 2: Bud having the pencil stuck up his nose and retaliating.  That led to him being locked up in the shed, which led to him running away.  

Main event 3: Bud meeting up with Bugs and the two of them going to Hooverville.  

Main event 4.  Deciding to search for Calloway and head to Grand Rapids

Main event 5. Bud meets Lefty Lewis who knows who Calloway is.

Main event 6. Bud finally meets Calloway and discovers that he is not Bud's father.  He is Bud's grandfather.