What does “make the leap into the Richmond (or any name of the place) fishbowl” mean?

The fishbowl is the fishbowl of public scrutiny.

The one in one of someone is the portrait.

So this is the portrait of a person unable to make the transition to a life wide-open to public scrutiny.

The image below (from fishbowl at yourdictionary.com) shows a fishbowl, as often used stereotypically to portray how visible fish are when they live in a transparent glass bowl that anyone can see through. Saying that Governor McDonnell and his wife are in “the Richmond fishbowl” refers to them being highly visible to one and all. Their privacy is limited because they are prominent public figures, at the top of the heap among important people in the Virginia capitol.

A fishbowl is a highly visible way of housing a pet such as a goldfish, because they are on display 24/7.

Richmond is the state capital of Virginia, and the "Richmond fishbowl" is a reference to the fact that being a governor (or first lady) of Virginia in Richmond is like "living in a fishbowl."

The comment was that the "portrait" of Mrs. MacDonnell "painted" by co-workers, was of someone unable to make the leap from "private person" to the "fishbowl" that a First Lady occupies.