The "backdoor" of Theodore Roosevelt N.P. (North Unit) is a great option if you are willing to do 10 miles of dirt roads. (From ND 68 eastbound stay straight onto county road 7 miles; turn right/south 4 miles on paved county road; then left 3 miles with zigs to park) It's easier to find heading east to west than vice versa. Also the gate is usually locked - which means lifting your bike over - usually easier to remove panniers, first. Most importantly, you better have a map and know your directions - esp. in hot or cold weather.
Could you be a little more specific to the directions, i.e. the starting and ending intersections or towns? I was looking on Google and MapQuest and couldn't find the paved CR that is 7 miles east of anywhere on ND-68. I was thinking you meant east on MT-23, south on Bennie Pierre Road/CR-202 which becomes CR-38 in ND, weaving thru the park and coming out near Grassy Butte, ND but couldn't be sure as at no point was "my" route on ND-68.