Welcome to the form. I am sorry to hear of your trouble with Bert. Situations like this can be very frustrating at times. Something I came across a few years back might be the answer you're looking for its called Ssscat Cat Repellant. It's a pressurised can of air with the motion sensor mounted on top. If it was put around the doorway when Bert went to go through it would hit him with a stream of air plus a hissing sound which would have a tendency to deter him from entering the room. The one problem is that it will not discriminate between cats so it will target Sasha as well as Bert.
Here is a product review of the item for you to have a look at and see if will work for you. If you do decide to go after the Ssscat Cat Repellant please let us know how it works. I never did get one but I did think it was a great idea for one problem Cat. The problem was there were four other cats that could be unduly affected by it.
This system beats the spray bottle. In due time the cat relates the spray to the bottle, and the person behind it. This way there is nobody directly involved that the cat can relate it to.
Best of luck finding a remedy for your problem, and hopefully there are some other members with ideas for you.