Benny Golson is a living legend, one of the few musicians alive who has not only seen the entire modern jazz era, but actually played a major role in the development of the art form. Although he is relatively unknown outside the jazz aficionado world, his influence has been immense. As a composer, he is probably best known for "I Remember Clifford" and "Killer Joe". But he has composed many great songs, including "Along Came Betty".
When you see the name Benny Golson on a piece of music, you will know two things immediately:
The changes are not complex harmonies, but they are less predictable than in many standards. There are several places where the music shifts up 1/2 step and then back down. These are important moments you find in measures 1-4, 9-12, and 25-28 -- or about 1/3 of the chorus. To get started improvising on this piece, it would be effective to find a comfortable line for measure 1 and then play that same line up 1/2 step in measure 2 and so on, then depart from that simple pattern as you get more familiar with the changes.
There really are no great shortcuts on a song like this. Just keep practicing it until everything comes automatically.
It is worth mentioning that this song is usually done as a medium swing. This arrangement is a straight-8th smooth jazz treatment.