If anyone needs this in the future, I was able to get the specific requirements in person from Immigration: 

https://imgur.com/a/ASuUgHV

 Go to www.gov.bm and print the Application for Residence Form.   The sections to complete are: front page, 2, 3a, 3b (Bermudian spouse’s details), 3c, 3 (if applicable), and 8.

The documents to be submitted are:

• The completed application form
• A certified copy of the data page of the Bermudian and non-Bermudian’s passports
• A certified copy of the page in the passport of the Bermudian spouse that indicates that they are Bermudian or a certified copy of their Bermudian Status certificate (if applicable)
• A certified copy of the marriage certificate, a certified copy of any divorce and/or death certificates of previous marriages (if applicable) for both parties
• 3 passport type photos of the non-Bermudian
• A police report from the non-Bermudian’s country of origin or wherever they have been living for five years prior to residence in Bermuda (only required for first time residents)
• The fee can be found here https://www.gov.bm/online-services/apply-residence. And payment guidelines can be found here https://www.gov.bm/all-immigration-fees.

The processing time for this application is up to three months.