Hi Dominic,
It's great to hear you'll be visiting this summer!
It is definitely possible to reach Benbulben without a car, though public transport options are limited. From Sligo, the closest bus route is the Bus Éireann Route 480 or 64, which runs toward Derry and passes relatively near the mountain (but it won’t stop directly at the Gortarowey Forest Walk Car Park, but at Drumcliff, from which you would still have a walk of close to 5km to reach the trailhead). You can check times and routes using tools such as Transport for Ireland's
Journey Planner or platforms like
Rome2Rio. Getting a
taxi from Sligo town may be the easiest option and the journey is only about 15–20 minutes. For the return journey, I'd recommend pre-booking a pickup time with the same taxi company or arranging for the driver to collect you at a specified time.
Hoping that helps with the planning!
Alex