@shindy,
The sentence is a little awkward. It sounds more natural to say "he got on the bus." That said, I don't think either are strictly incorrect, but they do imply different things. "He walked onto the bus" suggests that "he walked onto (the steps/floor/surface of) the bus." It might be more accurate to say something like "he climbed (the steps) onto the bus." This is kind of picky but people don't typically walk
onto things. They walk forward and backward, up down, and on things, but not really onto things. They jump, climb, and move onto things.
"Walked on" can be a phrasal verb that gives the impression of moving past something, material or abstract. In other words, "he walked on (from or past something) to the bus." I don't think that's what you were trying to say here though.