While answer A is grammatically correct, if you say "I am boring" you are saying "I am a boring person". You may very well be a boring person, but I am sure most people don't want to admit that they are a boring person.
"I am bored" or "I feel bored" are said if you have nothing to do and are feeling sad about it.
So how to use boring. Some examples include:
The new documentary on Netflix is boring.
My job is boring.
That teacher's classes are boring.
Some related idioms include:
Bored stiff - extremely unhappy because there is nothing interesting to do.
The children have been bored stiff staying at home during the Covid-19 pandemic.
Bored to death - I was bored to death during the during the hurricane because or internet and electricity were cut off.