Do I use was or were in this sentence?
Bonnie, along with her associates, was invited to the gathering.
The trick here is the use of the comma. Here, the two commas are used to provide additional, but not essential, information. Bonnie WAS.
They were. (Plural)
She was. (Singular)
"Bonnie and her associates" are "they" so you would say were:
Bonnie and her associates were invited to the gathering.
However, in your sentence, the associates are not part of the subject, so you would say:
Bonnie, along with her associates, was invited to the gathering.