Permission to transfer record to the ward that you don't live in

We live in Ward A but have been attending services in Ward B for the past two years. For some reason, we don't feel the spirit every time we attend the sacrament in Ward A because of some politics that is happening in that ward. The Bishop, who is so prideful and always saying hurtful words, not just to us but to other members as well, which we can no longer tolerate. We already talked to our Stake President regarding this matter, but nothing has been done. The Bishop can't humble himself., so instead of being an inactive member, we decided to go to Ward B instead. 

The President won't agree on it, but we don't want to deal with those kinds of people anymore.
They didn't even schedule a counseling meeting to fix the issue. They always say that they don't have time.

Is it possible to transfer our records to Ward B?

From General Handbook 33.6:

Membership records should be kept in the ward where the member lives. Exceptions, which should be rare, require the consent of the bishops and stake presidents involved. To request an exception, the stake president uses LCR to submit the request to the Office of the First Presidency.

Of course if you move into Ward B's boundaries...

It sounds like a difficult situation. Attending a ward that doesn't have your records isn't ideal because you won't appear on ward lists or class rolls, you won't be able to receive callings, and things like temple recommend renewals and tithing settlement can only happen in your own ward.

In general, Church members are counseled to attend the ward where they live geographically (or one of the overlapping wards where they live geographically – family ward, YSA ward, language ward, etc.). Transferring a membership record to a different ward requires approval of the bishops and stake president(s) involved, as well as approval from the Office of the First Presidency. For more information about seeking an exception, see section 33.6 in the General Handbook: https://www.churchofjesuschrist.org/study/manual/general-handbook/33-records-and-reports?lang=eng#title_number19

I'm sorry for your situation, there's definitely times where membership status in a ward is a complicated issue, and I'm certain you haven't made this decision lightly to attend another ward. However, as mentioned the Church has strict protocols regarding member records being transferred to a non-geographic other ward. I'm not certain politics or personal issues will be enough to justify the record move, even if these issues are real and hurtful.

I expect the most realistic path forward might be to continue to accept the limitations that come from attending Ward 'B' without your records residing there, and interact with your Bishop in Ward 'A' when interviews and such are required. I'm certain this will continue to be a heavy burden for you, but I don't believe anyone here in the Forum would have any alternative, beyond continuing to try and work with your Bishop and Stake President to resolve your concerns.

I'm sorry to hear of your difficult situation. We had some friends in a similar situation several years ago. I don't want to turn this into a gossip forum, so I'll just say a bad situation got worse and they ended up moving. We are imperfect people called to do the Lord's work, and, unfortunately, that imperfection extends into even high-ranking church leadership positions.

One option to consider is if there are any overlay language units. They could be in another stake. You might not speak the language, but might be able to transfer your records. Sometimes I've seen these other-language units have multi-lingual meetings with translation offered.

I don't know how old you are or if you have children at home. If you don't have little ones, maybe you can talk to your mission about serving a local mission, which will usually put you serving in a different stake. Of course, you'd have to talk to your bishop and stake president to get the call done.