Vent swelling goes in & out when goose honks - prolapse?

One of my geese -- 5 month old female brown Chinese - has something coming out of her vent to one side. It pops out when she honks -- roundish shape - maybe the size of a cherry tomatoe, but yellowish white color. She seems unbothered and is running around with her flock, and I was unable to catch her by hand -- even with the lure of watermelon -- she's FAST and definitely knew I was eyeing her. I am going to try to catch her this evening with my poultry catch net. I just didn't think it was worth chasing her when it is so hot outside and risking stressing her or possibly injuring her -- adding a broken leg to the mix probably not helpful.

So, my plan is to catch her tonight, bring her inside the house, then I thought I would soak her in a warm bath of betadine water in the tub and take her to the vet tomorrow. My vet will be the first to admit he knows nothing about birds, so any ideas for diagnosis / treatment that I could share would be greatly appreciated.