Hens first egg stuck in butt

Deep breath - a little more information will help here.
First, are you certain it is an egg? You mention that it is all bloody so it is possible what you are seeing is not actually an egg but a prolapse.
How long has she been attempting to expel the egg? Is she actively straining or does she seem to have stopped doing so? Passing an egg is not always a quick easy process and it is possible for it to take a bit without being a situation that requires intervention.
Is the egg a soft shell egg or does it seem fully hardened?
Take your bird inside and wash the area - this will give you the ability to see just what you are dealing with without the blood impeding your view. Washing with warm water can also help to ease the egg along. This step will allow you to better assess what is going on and determine the best next step. If the egg is truly halfway out you can use your hand and a little olive oil (or other safe lubricant) to try to GENTLY massage the distended vent tissue around the egg moving the vent back and the egg forward to finish expulsion. The tissue is stretched and easy to damage or tear at this point so use lots of lubricant and be extremely careful and gentle. An alternative would be to soak your bird in a warm bath which will allow the warm water to help relax the vent and add moisture to help move the egg along - this is more effective if your bird is actively straining to help move the egg.