This could be two people, but would normally be written with a different separator: "Betty, a maid; and a cook" (just removing the comma doesn't help because then Betty could be a maid and a cook). As-is, the implication is that this is three people. If you would like to make that more explicit, you would instead re-structure the sentence†, so it's not highly relevant to the serial-comma-vs-no issue.

†For example:

Betty, one maid, and one cook.

Betty, and a maid and a cook (a little awkward)

A maid, a cook, and Betty (depends on how you want Betty's inclusion to land for the reader)

Three people; otherwise it should be, "They went to Oregon with a cook, and Betty, a maid."

Or better yet: "They went to Oregon with a cook, and maid named Betty."