I have, I think, traced part of my wife's Bill/Bills family back to the parish of Willey. To take a broader look at the Bill/Bills family, I am currently going through all the Baptisms, Marriages and Burials for the family in Shropshire. FindMyPast has returned 426 baptisms and I am up to the Elizabeths in transcribing them fully and checking the images, so quite a way still to go.
My thoughts on the baptism in question were that Fiddler may be a location in Oldbury parish, and that the baptism was for a family not normally resident. However, the wording I am used to actually states that the father "was of the parish of ...", which makes me think he is possibly some form of intinerant. NLS have old maps of Oldbury, but only as far back as the 1880s, so tring to find somewhere called "Fiddler" may be tricky, unless older maps can be found online. I will check with the Shropshire FHS to see if anyone can help. The parish is adjacent to Bridgnorth, so a clandestine baptism may still be a possibilty, but I have never come across clandestine baptisms before, only marriages. I will look at this further.