It needs to be relatively flush with the vent. Did you try preparation H? It causes shrinkage and contraction of the tissues.
By the way, egg binding like this is often a sign of calcium deficiency. We can work on that with you, too.
Laying flocks should be on a diet that is mainly laying pellets which are designed not only to provide calcium in sufficient amounts for laying, but also the supporting nutrients that help calcium absorbtion. It's a good idea to also provide free-choice calcium supplementation for birds who feel they need more. There are various forms of this on the market. It should be provided in a separate container from their food. I use oyster shell granules.
But calcium isn't enough. The bird's diets must not be high in grains (in addition to those in the pellets) because grains are high in phosphorus. While phosphorus is necessary for calcium being absorbed, it must be in a pretty exact proportion to the calcium. (2:1 calcium

hos is the normal proportion). Too much phosphorus causes the avian body to extract calcium from the body, including bones, to make up for the need. Too mush phos will also result in soft shelled eggs, egg binding, and prolapse.
So 90% pellets, 10% treats and grains if you choose to give them.
The other most important part of providing calcium is vitamin D3. Vitamin D is usually found in feeds, but it's an oil vitamin which means it unfortunately can degrade in a dry non-oily source, with age of the feed, and in sunlight. If you suspect calcium problems in your birds, boost their D vitamins. Yogurt is a nice choice for this in small amounts as it provides calcium, vitamin D, and also living bacteria which help food use. Apple cider vinegar (organic only - not because of the philosophy but because of its make-up) is another good choice. It enhances calcium absorbtion and also provides enzymes, electrolytes, and living beneficial bacteria.
So when you get this hen on track, I'd give her a daily treat of yogurt, put some ACV in her water (1 ounce ACV per 1 gallon of water) for a week. Then do this occassionally during the month during heavy laying to keep things going nicely. I like once weekly or three days a month.
P.S. Be sure to clean the vent thoroughly to remove the blood. Preparation H will help with the fissures, tiny breaks, in her skin. When she doesn't prolapse anymore, try using a non-cortisone antibiotic ointment like Neosporin on her vent for a week.