It was close to her own accent, but she could certainly do the mid-Atlantic accent as can be heard in this clip from "Call Her Savage."
"This is java - but java."
Bow plays another circus performer in "Hoopla," her last film, in 1933, with an accent closer to her own.
What's really interesting about the role is that it would have been perfect for Mae West - Bow plays a wise-cracking vamp who falls for an attractive young man. In fact the role is the Mae West character - West really never played any other kind. Bow's character is even named "Lou" and West played "Lady Lou" in "She Done Him Wrong" also released in 1933. Based on the few films I've seen of either of them, I'd say Bow had greater range as an actor than West, but on the other hand, West wrote many of her own wise-cracks.
West was almost a decade older than Bow, but West spent her twenties and early thirties in New York theater, producing, directing and starring in plays she wrote herself, and getting arrested for them.
West didn't get to Hollywood until 1932, at the end of Bow's career and the beginning of the dread "Hays Code" which cracked down on naughtiness in Hollywood. Since all of Bow's movies were pre-Code, she got to show a lot of skin, including at least two films where she is seen skinny-dipping, including Hoopla. If it wasn't for the Hays Code, you know West would have tried to top Bow for who could be the naughtiest.