I'm not clear from your question whether you're sure your ancestors were non-conformist, or whether you're assuming it because there wasn't a very local C of E place of worship at that time.
If you're sure they were non-conformist, do you have anything else giving clues about which chapels or denominations they may have belonged to?
Pre-1837 non-conformist registers are mostly held by the National Archives, and images are available at various places online. I've found births of children to a Job and Mary Jagger and to an Abraham and Hannah Jagger, both at Clayton Baptist Chapel in the time frame you mention.
The Old Dolphin chapel was Wesleyan, and they would have practised infant baptism. Another place to consider would be the Kipping Chapel in Thornton (Independent/Congregational) - I'm pretty sure their registers are online somewhere, but transcripts are also available from Bradford FHS.
There are other Yorkshire non-conformist registers at Ancestry - mostly post-1837, but I think there are also some that weren't deposited in 1837.
On the other hand, if they were C of E then they might have attended the Old Bell Chapel in Thornton. But all these places were within the ancient parish of Bradford, and the main parish church (St Peter) registers contain baptisms from all parts of the parish, including Clayton. Baptisms at the Old Bell are often recorded both there and in the parish church registers.
Just in case Jarvis's baptism was missed, could you tell us his parents' names, please? That might help us look for siblings and provide useful clues.