The phrase 'busiest month' is correct and can be used in written English.
For example, you could say "January was our busiest month this year, with an unprecedented number of orders."
And the Knicks closed March — their busiest month of the season, with 18 games in 31 days — with a rather impressive 12-6 mark, despite losing Tyson Chandler for the last 10 games.
The museum's busiest day of 2013 was Friday 16 August, with 33,848 visits and the busiest month on record was July, with 747,936 visits.
In fact, November was the busiest month CAP has ever experienced.
In December, traditionally the busiest month for shopping, same-store sales were 8% lower than in December 2005.
"January was the busiest month we have ever had, which is a really good sign for this year," Mrs Smith said.
July is the busiest month for Yellowstone National Park.
The key holiday airports are anticipating the busiest August bank holiday on record.
This is their busiest January yet and to celebrate, they're hosting a Burns Night to remember.
The disruption comes at the start of what is expected to be the busiest November in aviation history for London's airport system.
Aberdeen Airport has reported its busiest October for five years, following a surge in international traffic during the school holidays.
"We have got probably the busiest March anyone has ever known in football [with eight games] and it will be all hands to the pump.
