Changed to Thursday evening.
Off-highway vehicle trail. Surface is dirt, grass, and gravel. A variety of bikes would work: some recreational or hybrid bikes (provided you are comfortable going off pavement - similar surfaces to the Hogue Island ride), cyclocross, or mountain bikes. Map http://www.parkrec.nd.gov/activities/attachments/roughridermap.pdf
Meet at the northern end of the trail 12 miles south of the intersection of Main Street and Highway 1806 (6th Ave NE) in Mandan, near 1503 Little Heart Bottoms Road.
Bing provides better directions than Google http://binged.it/1k2VQ0p
Here's some narrative along with the directions: proceed south from Mandan on 1806 and go 4.5 miles south of the Ft Lincoln State Park entrance. Cross Little Hear River (no sign, but it is a highway bridge), just after that there will be corrals and a loading chute for cattle on your right, then almost immediately after that, make a left onto Little Heart Bottoms Road (unmarked, but it is a gravel road going through a notch in the old railroad embankment - see photo below). Go through the notch then park in the dirt loop immediately to your right.
We'll go south a ways and back the same way. We'll discuss how far south based on who shows up and the weather. We may make a small diversion to the Little Heart Bottoms Boat Ramp, 1549 Little Heart Bottoms Park, Schmidt Bottoms Road (paved road- public boat ramp- boat dock- parking lot- vault toilet- trash receptacles), just for future kayaking, biking reference.