I now have more productive time during the day because I keep the office gossips_____.

The speaker in this sentence expresses a positive outcome (more productive time) and then explains the reason (their intentional distance from office gossip) . The appropriate phrase would be one that suggests distance or avoidance and is preferably idiomatic in nature. 

At arm’s length (Option B) perfectly fits in this context of avoiding office gossip, as the phrase essentially means maintaining a safe or cautious distance, especially from people or influences you want to avoid

A foot away (Option A) is literal and lacks the idiomatic meaning needed. (It literally means to keep gossip one foot away, which makes no sense as gossip is intangible.) At bay's length (Option C) is not an actual phrase. Out of harm’s way (Option D) means keeping something safe, which doesn’t fit the idea of avoiding gossip.

The correct answer is, therefore, Option B - at arm’s length.