Usually in cases like this, the most important events of the story are already covered in the Anime, so you wouldn't really miss anything. I mean, if you start reading from chapter 1, you'd probably only find minor changes that were made in the Anime that wouldn't really change what you've already learned so far in the story.
In other words, yes, it's probably safe to start reading at chapter 110 or whatever the manga equivalent of the season 1 finale is. However, if you really want to know the differences between the manga and the Anime, you should start at chapter 1.
I haven't seen or read Arakawa Under the Bridge x Bridge by the way. I'm simply saying all these stuff based on experience.