Generally bathrooms are the smallest rooms in the house. This makes it a challenge to bring in more light. You don’t want to sacrifice privacy but you will want enough light to brighten the room.
If possible, create your plan before your house is built if you a working on a new home. If the bathroom is located on the south side of the house, it will get the most daylight. From sunup to sundown, the light will reach your room.
Try to plan for larger windows. The design of the room will determine if this is possible. If the exterior walls don’t have the fixtures located on them, you can possibly have a larger area available for windows. While you will pay more for larger windows in the beginning, you will save over time by using less electricity for lighting the area.
You can use overhead windows such as skylights to brighten the area without losing the privacy you desire. If you can locate windows at opposite angles, you will have cross lighting. Floor to ceiling windows or doors give so much daylight. If you use glass blocks or acrylic blocks, you won’t loose the privacy you desire.
Another possibility is to use shutters or translucent pleated shades that can be adjusted to allow for more light entering your room. The possibilities are there and some will save you money in the long run.
When improving the bathroom in an older home, you can use some of the above ideas to help. I would suggest reading magazines related to this subject and doing some online research.