The BM1-5 express bus routes do not operate on Sundays. NYCT has Good Service on them.
In past years, NYCT would post virtually every bus service alert related to the West Indian Day Parades. Although I didn't get a chance to retrieve any alerts regarding to the parade until 7:30 PM tonight, I did manage to check NYCT Buses Twitter page for their history. The only alert received was for the B12 bus rerouted to Lincoln Road due to NYPD activity. Apparently, all day, there were no bus service alerts for the B14/17/41/43/44/44SBS+/45/46/49 bus routes - - all which pass through Eastern Parkway. Also, note in the screenshot below that B67 buses are detoured around the Brooklyn Navy Yard - - there is no weekend service on the B67 north/east of Sands/Jay Streets.
The B41 buses were "running - - not!!! And scratch your heads at the next service alert below it - - it runs from 6 AM to 10 PM everyday.
This is why NYCT cannot be trusted to provide timely, accurate and consistent planned and unplanned service alerts. They clearly were taking a holiday today. On that note, I hope your summer was blessed with happiness.