Ok I'll start this off by saying yes there is a chance that Bege shot Bobbin but some folks are acting as if the manga has specifically stated that it was Bege, which it hasn't because the figures were shadowed. Signs are pointing to Bege staging a coup so it could very well be him. He did attempt to take out Pekoms, and the way he did it leans toward it being more of his idea that Big Mom's as I am sure she could've gotten use out of his remaining years. I do think that most likely Bege will be the culprit but I wanted to put a few other ideas out there.
My first idea is that it was a group of the Germa 66 clone soldiers. Now I am aware that the soldiers are meant to obey every order but I am gonna say that a group or all of the soldiers will stage their own coup. I am saying this because I think that a very important part of the Germa clone soldiers life is that they are relatively normal beings. I think there there is an important reason that they are not aware that they are clones. I am going to say, if this theory is true, that someone has clued them in on the fact that they are clones and they are setting up the Vinsmoke up to be killed as a result. We have seem that the Vinsmoke treat people the deem lower horrible. Lets say a worker finds out the secret then shows a soldier, it could spread like wildfire. Or maybe one of the scientists has a side deal with Big Mom? And the Vinsmoke family seems pretty overconfident as a whole so it would nice to see their faces if this happens.
My second idea that I thought of while writing this blog is that the culprits could have possibly been prisoners realeased from Big Mom's library. I thought of this while writing about Bege because there seemed to be someone possibly related to him being kept prisoner. If a person is important enough to be kept prisoner by Big Mom I think that it is safe to say that they have some kind of worth, and like Luffy may be strong. After being released I'm sure there are some that were recaptured, some may have been able to flee, and others ready to take revenge. The last group are the ones who I believe could have possibly decided to begin their payback with Bobbin. Like I said I thought of this one while writing this so it needs to be fleshed out a bit.
Random theories, let me know what you think or if you have any of your own. Lastly and most importantly, whatever happen to Caesar Clown???