There’s a trail at Powder Mill Lake, on Rocky Lake Road, but I haven’t been on it in a year or two. I think it will eventually get connected into the Shubie Trail system.
There are dirt jumps in Fall River and Wellington, if you’re into that sort of thing.
There may be some nearby ATV trails that you could get on, but they probably aren’t maintained, and would be in rough shape for mountain biking, but maybe doable. I’ve ridden the trail at the end of Old Holland Road, and the ATV trails behind the park across from Oakleaf Crescent many years ago. I have no idea what shape they’re in now.
Most of us drive to the trails around Halifax, and there are many within an hour’s drive or less from the city. I have a small SUV with a hatchback. If it’s just me, I just throw my bike into the hatch. If there are two or more of us, with saddles out, and front wheels off, we stand the bikes up.