If relying on rail transport, commuting from either Castle Cary or Taunton is an option. However, you specifically mentioned Bridgwater. There would either be a commute to Bristol or Taunton by train to change for London. I do know of people commuting daily to London, yet not from Bridgwater.
It would be incredibly helpful if you could share with me your preferred area to relocate to? If unknown, will you be regularly returning to London, if so, would access to the M5 or A303 be of benefit, perhaps the rail network is important to you. What are your hobbies? Do you have specific requirements such as schools or individual interests? My role is to support enquiries such as yours and help you to identify the appropriate location to consider. We recognise Somerset as a well connected county, which is so often passed through by businesses and those looking to relocate. Having lived here my entire life, I know they are missing a treat and a fantastic opportunity.
If you are able to provide me with additional information, I will then be able to support you much better.
Somerset is rapidly moving on from the hippy, cider, cheese image with many household names manufactured. Probably the most important message is that connectivity is good and the costs associated with living, or running a business are substantially less than some areas of the UK http://www.intosomerset.co.uk will give you a good insight as to what is here.