Not Arsenal I would say Orient are probably the nearest. Although south of the river could be Millwall or Charlton.
As already stated, the Bow Bells were not in Bow. Also it is within the sound of the Bow bells, so distance and area can be confusing.
A study was carried out by the city in 2000 to see how far the Bow Bells could be heard, and it was estimated that the bells would have been heard six miles to the east, five miles to the north, three miles to the south, and four miles to the west.