Rev Nathan ANDERSON, Methodist Minister, 1770s
Normally I do not answer such questions as the link with Hertfordshire is not established, and there is so much vague and often incorrect information emanating from the USA about English origins that it is easy to be led up the garden path.
Basically, if a marriage is not listed in the LDS indexes and you have no idea where it took place, possibly not even in England, the only thing you can do is to look for other evidence about the individuals - avoiding reliance on any "about" information on the IGI index on familysearch like the plague (see The Limits of the IGI on Familysearch).
Assuming the names (but not their exact spellings) are correct a search of familysearch for register transcript entries come up with only two likely baptisms in the whole of England:
Nathan Anderson, baptised 18 MAR 1742 at Flitton with Silsoe, Bedfordshire
Martha Purrier, baptised 03 NOV 1745 Elstow, Bedfordshire
Elstow is a small village just outside Bedford alongside the main road from London that ran through Luton. Silsoe is a small village on the same road halfway between Luton and Bedford, about 7 miles from Elstow. To make matters more interesting Wesley preached at Bedford on 17th March 1758 - when Nathan would have been at an impressionable age.
I am also aware that Wesley visited Luton in 1772 and recorded his visit thus:
"Jan 16th I set out for Luton. The snow lay so deep on the road that it was not without much difficulty and danger, we at last reached the town. I was offered the use of the Church. The frost was exceedingly sharp, and the glass was taken out of the windows. However, for the sake of the people I accepted the offer, though I might just as well have preached in the open air. I suppose four times as many people were present as would have been at the Room: and about an hundred in the morning. So I did not repent of my journey through the snow."
The Story of the Churches in Luton, Rev F. C. Hamlyn
Without any alternative suggestions this could well be your couple as both names are very uncommon, they would have shared the same market town of Bedford, and there are even possible opportunities for Nathan to hear John Wesley preach.
As the earliest Wesleyan Methodist chapels in Hertfordshire were in the north of the county close to the Bedfordshire border at Baldock, Harpenden (just south of Luton) and Stevenage, it is not impossible that this Nathan had some Hertfordshire connections - while Herefordshire connections are geographically very much less likely.
Obviously you will want to follow up the Bedfordshire connections, which is beyond the scope of this site. For information relating to a possible link with Hertfordshire you should try HALS. They have an extensive card index and if, for example, Nathan was a Methodist minister before he left for America there might be a record of the registration of a private house for a meeting places. Even if you could establish a Hertfordshire address this would probably not help with the marriage. A Methodist minister would not want the humiliation of being married in the Church of England church in the town or village where he lived, and many better off non-conformists went to London to be married where they were not known.
Outside Bedfordshire and Hertfordshire you would be best advised to search for Nathan Anderson in the early Methodist records and the best place to start would seem to be the Methodist Archives and Research Centre at the John Rylands University Library of Manchester. Unfortunately Nathan Anderson is not included in their list of early Methodist ministers, but they may have other relevant information.
If you can add to the information given above tell me.