Bully now days is becoming a serious and big problem because it often happen in many places. Even thought there are many media shows this cases, it still there are many other cases of bullying. It seems very difficult to stop. If it happens to us in work, we just need to stay calm and be deaf. They will not stop bullying us because they who do bully is such as animal, they don't really have heart or even they have completely lost their mind. Actually, when they bully others it means that they are bullying them self.
Don't allow them being you down. Laugh with them if possible. Be better than they are. Act professional and don'tmind whatever they say.
I think it is hard for us to really adapt op's situation but from what i see, maybe they are bullying for a good job you did, or they are testing and even they just are curios on your relationship with higher ups. Sometimes it depends on how long you are working but if they want you to leave the job just for their personal gains, then i think you should be able to read and learn how to address that bullying.