There are several places named Bristol in New York state. Bristol Center is about 4 miles southeast of Bristol, and Bristol South is around 6 miles south of Bristol Center. Around 1.5 miles to the southeast of Bristol South is Bristol Springs.
The town area was first settled around 1788. The town of Bristol was formed in Ontario County, NY, in 1789, but the first town meeting was not held until 1797. It was named after Bristol county, Massachusetts, so only indrectly named after Bristol, England. In 1838 part of the town was used to form the town of South Bristol.
Bristol Springs was settled in 1812.
A walk to the Burning Springs of Bristol (Daily Messenger)
Bristol & South Bristol (Visit Finger Lakes)
Bristol Hills Historical Society
Bristol, New York (Wikipedia)
Early History of the Town of Bristol (Bristol Hills Historical Society)
History of Bristol (Genealogy Trails History Group)
History of Ontario County (Daily Messenger)
History of the Town of South Bristol (Wayne County NYGenWeb)
South Bristol, New York (Wikipedia)