I am indexing a marriage contract, and the brides surname has 2 spellings, should I put the one that the bride wrote?
No, you should index both versions of the surname (in this case), separated by an Or.
See the last section of your instructions - General Indexing Guidelines - under Alias Names
If alias names were included on a document, or if an individual's name was listed with various spellings on the document, include all variants, separating each with the word Or. For example, if a name was written as "Georgios (George), George Broski, George Browzowski, or George Brzozowski," index the name fields as follows:
Thank you very much. I appreciate it.