Actually it's not a too far-fetched idea. Judging from how we Arabs and Iranians conduct ourselves when issues of mutual interest are discussed this is not such a crazy idea. I also understand that no world power is going to trust any leadership of the region 100%. Look at my post number 22 in this thread for further explanation.
As much as I have a lot of respect and admiration for many of the Nations in the Mideast (Saudi Arabia, Iran, Iraq, Jordan, UAE, Bahrain), I believe that there are areas where extremism and ultranationalism can cause a powder keg. The lessons we learn from the Syrian conflict is just too real, to close to home. The GCC region is a strategic value area, given its massive energy supply role. A conflict here would devastate the world economy , and thus whatever means can be done to guarantee a prevention of crisis proportion should and must be realized. The British Navy's permanent presence here helps to make the region ever more stable.
Off course it is our business. We regard this is as a security threat. What nation would not prefer to NOT have foreign military bases in its immediate neighborhood?
Obviously the Bahrain regime (and the rest of GCC for that matter) looks at it from a different set of glasses, as they rely on foreign powers such as the UK and US for regime survival.
There is a Japanese proverb that bears significance in this context: 挨拶は時の氏神
It means, "The presence of Arbitration in a quarrel is a gift from God".