Feng shui cures that work have to be really liked by you and make sense in your overall home decor style. If you bring a so-called powerful feng shui cure that is supposed to work but looks totally out of sorts in your space, it will not create good feng shui for you, maybe even quite the opposite.
The reason mirrors are sometimes recommended in feng shui for the bathroom door is because a mirror can make a wall or a door energetically disappear, so to speak. A mirror also pushes the energy back; this is why, for example, it is always recommended to avoid a mirror facing the main door.
A mirror outside the bathroom door is sometimes used in feng shui as the mirror pushes the energy away from entering the bathroom, thus the energy is prevented from going down the drain. Bathrooms have a bad reputation in feng shui, so a mirror on the bathroom door became a popular feng shui cure for it.
You have to decide for yourself if a mirror on the bathroom door is something you would like in your home decor scheme, and if it makes sense to you.
Bathroom Feng Shui Cure
The main feng shui cure - and the most solid one - to neutralize the negative energy of a bathroom is to actually take good care of your bathroom. If you focus on creating good energy in your bathroom if you transform your bathroom into a beautiful spa - why would you need protection from its energy then?
There are many ways to create a bathroom that has a clear, fresh and nourishing energy, you just have to put some time and effort into creating good energy, and then maintaining it. If you do love mirrors, the best place to have them is not on the bathroom door, but actually in the bathroom.
Mirrors bring the feng shui energy of the water element, and this is excellent for any bathroom as it cleanses - energetically speaking - and refreshes the stagnant and stale energy. Busy bathrooms create a lot of low or challenging energy quickly, so instead of trying to pretend that there is no bathroom there - which is the goal of placing a mirror on the door, deal with the energy of the bathroom in the first place.
Another point to consider is this: when you place a mirror on the bathroom door, you actually make the door disappear, too! Doors are important in feng shui as energetic guardians of any given space, they create good containers for specific energies.
So no, you definitely do not need a mirror on the bathroom door in order to create good feng shui in your home. You just need to take care of the quality of feng shui energy in your bathroom.