You can catch the Broome Explorer Bus to the Courthouse and Night Markets from all major accommodation.
Courthouse Grounds (Stop #12/33):
Saturdays: 8:00am – 1.00pm all year round,
Sundays: 8:00am – 1.00pm from Easter Weekend to October
Night Markets – Town Beach Reserve (Stop #6 / 39):
Full Moon Nights: From April – September. See above for Staircase dates return times link.
Every Thursday: June to September. Return times from Town Beach bus stop = 5.55, 6.25, 7.25