Okay, a few things may be going on here.
In both scenarios you said they were fine for a few days and displaying like crazy in the mirror. Betta are extremely territorial. Another male triggers a kill or be killed response. The little fellows have been spending ALL of their energy trying everything they can to scare away the threatening male that is looking just as dangerous as he is, but its not working. I liken this to a stranger hanging out in your kitchen with a loaded gun aimed at you and you can escape. The harder you try to scare him away the more violent he gets. Do you see where I'm going? Those stressed out fish are wearing them selves out to the point of not being able to handle illness.
Where is the illness coming from? Simply from being a small environment the water chemistry is vastly more unstable. I'm not sure if you've been trying to feed them, but chances are the food is mostly going uneaten. Even if they do eat it might not be getting digested. Fish physiology is different than peoples. Fish have the ability to shut down parts of their systems in times of emergency survival. Digestion is one of them. Kill or be killed is one of those times.
In addition to the stress, unstable water chemistry and suppressed immune system is the fact that fish are poikilothermic, which means they are cold blooded. Their body slows with the cooling of the water they are in. A vase is not heated. Bathrooms usually aren't heated. Worse yet is the dramatic temperature swings that happen. Betta are more tolerant than most fish of temperature swings because of where they evolved, but a bathroom is too much. They also prefer warmer water all of the time, like in the low to mid 80's. I've had Bettas live 7 and 8 years.
Someone mentioned that Bettas breath atmospheric air. That's true. Do they have to have access to the surface? Its a good idea. They only breath atmospheric air when the oxygen content of the water is too low. Unless you are willing to get an oxygen meter and monitor the water several times a day, then it make more sense to just allow them access and let them deal with it themselves.
I've also had Betta imported from Thailand. Are they any healthier than
Walmart or
Petco's Bettas? Not necessarily. When it comes to the Walmarts and Petcos of the world fish generally are likely to have more health issues than if you buy fish directly from a breeder. I'm not dissing those stores. They just have fish coming from a multitude of locations and aren't setup to be able to quarantine fish. Betta are the one type of fish that doesn't always fall under that health risk issue that the other fish do. The reason is they are shipped in water and generally are kept in it so there isn't a disease cross contamination issue. You're likely going to get very healthy Bettas if you get them in their little cups (which aren't designed to be their homes) when they first arrive at those fish and pet stores. After the Bettas have been hanging out in those cups for a few days, next to other Betta cups, they are going to be subjected to the same kill or be killed stress as those in the vase in the bathroom.
Spring water. You don't have to dechlorinate it. There's no chlorine in bottled water. Tap water is actually healthier once you've neutralized the chlorine and chlorimines. Regular old tap water has minerals in it that fish need to produce healthy bones and tissue.
You're right about the dishwasher idea. You don't need to. A common mistake many people make is keeping fish's tanks (or vases) too clean. There are beneficial bacteria that colonize all of the surfaces that are under water. Those bacteria clean the water. Occasionally we need to go in and thin the bacteria out or it actually will start over populating itself and start killing itself off, which pollutes the water.
Oh! You mentioned burrowing in the roots of the bamboo. That's not burrowing, that's hiding from that killer Betta in the mirror.
Ummm, about the tiny fancy goldfish. There's no such thing. Black moors and other small goldfish you get are just young. They normally grow to at least 5" long. Ones that don't have stunted growth because of small environments and often in conjunction with poor water quality. Goldfish would be able to handle the temp in the bathroom and not get stressed out by the mirror, but a vase is just massively too small.
If you want something that will work in the bathroom in a vase with a live plant, I recommend getting some freshwater shrimp. Red cherry shrimp, to be exact. You can house 4-6 in one of those vases. They don't mind it being unheated and could care less about the mirror. You won't find them at
Walmart and its quite doubtful that
Petco will carry them. If you find an aquarium club in your area your best bet is getting some from a local hobbiest. Stores that sell only fish are likely to have some. Another beginner freshwater shrimp option is ghost shrimp. They are cheap because they are usually sold as live fish food. They are a little bigger and may not handle the transition as well as getting some juvenile RCS (Red Cherry Shrimp). I think shrimp are just as fun to watch as fish. They eat fish food so you don't even need to get anything fancy to feed them. Change about 1/8 of the volume of water a week and you're good to go.
Sorry the Betta didn't work out. It would have looked cool.
Good luck!