We tend to view regency fashion and manners through the prism of the later Victorian period. This tends to put things in a more, ahem, prudish light than is quite appropriate. Undoubtedly, while young females had companions and manners made strolling alone with a pleasant male companion difficult, there were aspects of fashion and manners that were more fluid than we’d expect.
Gilray’s cartoon satirizes the fashion of 1807, with its sheer muslins. Bombazine is a heavy black cloth, usually worn in first mourning and widowhood. Bum-be-seen, is something else. I’m sure the woman on the right is fully aware of what she’s displaying, and why.