Yeah I wouldn't use a bungee, they just pull the horse's head down, where as the pessoa encourages them to use their hind end. However as Spider said, direct work in walk and do far more harm than good and I'd be worried if you extensively walked her in the pessoa that the walk may become lateral, and that is a hell of a problem to try and resolve.
I have found that the best solution to horses with walking issues, is to get them out in a trail. Let your reins out onto the buckle. Don't let her dawdle, that will achieve nothing. You want a forward marching walk. Try to get her out on a trail a few times a week initially. I have found every horse I've known with walk issues to become so much better after a few rides out. They're more willing to go forward and have found that 4 beat movement that is much more comfortable.
I am having a few walk issues with my TB boy, he's recently ott and I've found he has a lovely walk, but if he gets tense it very nearly becomes lateral. So at the moment I'm not even worrying about having him on the bit in walk, if he's jig jogging and tense, falling all over the place I just let my reins right out, put my leg on and make him walk until he is reaching forwards and down, and tracking up.
I very rarely touch him in walk, I do all my serious work in trot, and from that he usually picks it up in walk quite quickly. I think your mare may be similar to my Hugo, so I'd certainly give a few trails a go and then every time you ride her for the next month, let your reins right out in walk and make her go forward. If she trots a little, just politely ask her to come back to walk. She'll figure out that it's easier to walk and you'll soon lose the jig jogging.