For your current situation, $150 to $200 a month is hard to justify. Nine transactions a year means your bookkeeping complexity is essentially zero, and your accountant is already handling the one moment where accuracy actually costs you money if it goes wrong. The monthly records a bookkeeper would produce would show you the same rent deposits and water bills you already see in your bank statement.
The assumption doing the most work in the "get a bookkeeper anyway" argument is that clean monthly financials create optionality, meaning a lender or partner can see your history clearly if you decide to use the property as collateral or bring someone in. That is real, but with a paid-off duplex, no debt service to track, and no partners, there is nothing to serve that optionality right now.
Where bookkeeping starts earning its fee is when you add properties or entities, because you get cost segregation across multiple assets, expense allocation between properties, and intercompany tracking that your bank statement stops being a reliable substitute for. Your accountant is likely doing light-touch categorization once a year to produce the Schedule E, and that works at your scale because there is nothing to misallocate.
The risk you did not mention is that the simplicity you have now can mask a slow drift in expense tracking if anything changes. One insurance renewal, a repair, a partial month vacancy, and the "nine transactions a year" figure starts climbing without a clear record of which year the expense belongs to. That is still manageable without a dedicated bookkeeper, but it is worth building the habit of a clean monthly spreadsheet yourself, even a basic one, so you are not reconstructing the year for your accountant from memory.
At one paid-off duplex, a bookkeeper is a cost without a return. The math changes when the second property comes in.
What is your current record-keeping setup between the bank and the accountant?