A little info on the family- Henry Kershaw from Long Marton married Maria Ridley from Askham and James Kershaw was born in 1841 also in Askham. He married Jane Surgeon in 1871 and moved to Gateshead in 1878 and started Kershaw Mineral Water Business. His sons - John James Kershaw, Wilfred Gladstone Kershaw, William Surgeon Kershaw and Walter Ridley Kershaw - were all involved in the business after James death in 1901
By the look of the seam I'd have to say that what you've got there is an early machine made (ABM) soda bottle
The crude nature of the bottle and all the bubbles would suggest a date in the 1907 to 1920 range. Do you know if the company was still in business for that long?
Just a couple of points on this thread which I thought might help.
James Kershaw was born in 1840, he died 2nd April 1906. Therefore, this bottle is post the 1906 date as prior to that the company was J Kershaw & Sons, after his death it became just "Kershaws". The company continued until 1965, run by the grandchildren of James. I'm his great great grand daughter.