I would say that the complete form is "Mir ist es langweilig," or (subject first) "Es ist mir langweilig." Use of the dative "mir" in this context implies that it's relative to your point of view, so there's no need for "bei". The "es" is the impersonal "es", and it's meaning as "the situation" is also implied by context. The impersonal "es" can often be dropped and usually is when it can be; it's function is mostly to be a grammatical placeholder for a subject when a subject really isn't needed for the meaning. English has a similar impersonal "it" though it's usage is somewhat different and it can't be dropped in English.
The reason I started with "I would say" is that that's how I interpret it, and I know there are other interpretations such as the one given in the previous answer. To me, "es" as the subject explains why "sein" is conjugated in the third person singular.
I'd add that you're looking at the sentence from an English speaker's point of view. Every language has it's own way of dealing with situations that don't quite fit the most common grammatical pattern. I'd also note that if you try to phrase it as in English, "Ich bin langweilig," it means "I'm boring," which is probably not what you want to say.