There is nothing that can be done about a cat that likes to bully other cats, short of either 1. killing it...or 2. making it impossible for that cat to physically approach the other cats.

I do not recommend killing the neighbour's cat. Therefore, either live with the problem or find a way to make it impossible for the Burmese to get near enough to your cat to bully it.

For some things, only time is a solution.

The nicest cat we ever had was bullied into a rapid health decline and an early death (through illness) by another cat we had who was an outright aggressive bastard who lived to beat hell out of other cats. In retrospect, we should have gotten rid of the aggressive one, but my parents did not recognize how serious a problem it was until too late. I was quite young at the time, and that's all I can remember about it.

Neutering causes some cats to be less inclined to aggression...but it's no guarantee.