The current understanding is that the Bowe and Bowes surnames in England represent different and unrelated families.
UK by County Per 100,000

Northern England by County Per 100,000

Southest England by County Per 100,000

Southwest England by County Per 100,000

Northeast England by Poor Law Union Per 100,000

Northwest England by Poor Law Union Per 100,000

Scotland by Counties Per 100,000

These maps were created using Archer Software's The British 19th Century Surname Atlas CD.