Hi again
Had a quick look at William's (1713) siblings just in case there was any clue, again on freereg and all bap Bridgwater, parents Thomas & Sarah
Ann 18/5/1705
Robert 9/6/1721
There are some transcriptions as well as freereg,
http://www.paulhyb.homecall.co.uk/index3.htm covering Bridgwater.
There may be further clues on William and Sarah Speed's marriage record in Ansford or maybe in their children's baptism records (nothing on freereg, but there are children on IGI, Meriam 15/11/1753, Sarah 27/2/1744 and Thomas 22/4/1751 bap Ansford, the Thomas looks good - first born son named after William's father?). Maybe someone could do a look up in Ansford registers for you.
There is a local forum which covers Ditcheat
http://groups.yahoo.com/groups/whitstone/ so you may get help there.
With what you have so far, it does look like Thomas & Sarah are William's parents.
All the best
Shirl