Seems to be some confusion between towns and counties?
Dorset and Somerset are counties.
Poole is a town in the county of Dorset. Nowhere near Somerset; nearest point some 55 miles away..

Bristol is usually identified as being in Gloucestershire.
But, some suburbs were originally in Somerset, and changed to Bristol in the 1930's.
Being pedantic, The City and County of Bristol was declared a County Corporate in 1373.
Even today not recognised as such by the Association of British Counties!
I was born in Bristol, and grew up in Somerset, just outside Bristol!