There are hairpieces that are glued on, they will stay in place for longer times and need to be cared for by a hair specialist, I believe. They do not cover the whole head like a wig, but just bald spots that exist. The downside of them is apparently that they will damage what little hair is growing in the spots they sit on, so once started and used for a while, they need to become a permanent solution. How big is the damage that is done and how long ago did it happen? If the main loss occured within the past 10-15 years there are some chances of getting that back.
As for the bathroom mirror situation - I think this happens to many - hair or no hair issues. I guess the only thing that helps there is to place the mirror in a way that you can do something before you have to look into it. Putting on a bandana or wig for example.