Just to put forward a different view, if I were in your shoes I would definitely get the marriage certificate, or even better, order the film of All Saints' marriages through the LDS family history centres (I have assumed you are not within easy reach of Newcastle upon Tyne itself). See
www.familysearch.org for how to set up an account and order on line. According to the link provided by Carole the film number is 847909.
Yes, there is a good chance that you will learn nothing new. But you might. The witnesses may be family members who could lead you to another snippet of information. The addresses might be helpful - you just never know until you see it. You might find that young as he is, your ancestor was a widower when he married Mary Ann. If you view the film of the register, there is a tiny chance that perhaps there is some info written there that is crossed out and so did not make it to the certificate you would get from the GRO. I have seen all sorts of notes in registers and those of us with illegitimate ancestors have to collect every scrap of info we can gather.
I accept that some have different views, but although I am relatively new to Rootschat I have been pottering away at my family history for some time and again, if I were in your shoes, I would make sure I had every certificate available for John and his mother. I understand that certs get expensive but it is so easy to go awry if you don't take care and document each step as far as possible. Death certs can also be helpful. An informant on a death certificate can be a clue to a family connection that you may not have been aware of.
It is cheaper to order certs through the General Register Office rather than through commercial sources - apologies if you already knew this. Here is the link
https://www.gro.gov.uk/gro/content/certificates/BTW, this link will tell you what you can find on the certs - you have to scroll down a bit
https://www.gro.gov.uk/gro/content/certificates/most_customers_want_to_know.asp#FamilyHistoryOrdering films of church registers through the LDS is the cheapest option of all, especially as you can pick up other family marriages, but it is slower. If you have a look at the on line film catalogue for Newcastle upon Tyne, there is a film of Bastardy Bonds for Newcastle although from memory it is mostly maintenance orders. These name the mother, the reputed father, and the amount the latter was obliged to pay for his child. Only the tip of the iceberg in terms of illegitimate children, but you might strike it lucky and find some information. Unless the name Bowie has a connection through the mother's side, it may be an indication of the father - just something else to explore and test.
Good luck
