The River Trail in North Little Rock is currently flooded from the pavilion at the NLR foot of the Big Dam Bridge and from the soccer/ deer field gate. The Isabella Jo trail is flooded for about 20 yards from the Cooks Landing road. Even if you got past there to the Campbell Lake Trail, you won't go far.
The road from the Cook's Landing Park to the BDB is open so you can get to the bridge. Riding options from Cook's include the North Shore Business Park, crossing the BDB to LR, or heading out Crystal Hill Road. There is some good climbing to be done by taking a right off of Crystal Hill Rd. at the Summit Church and going up to the SouthWind subdivision.
Riding from Downtown will allow you to cross to LR or get your kicks on Fort Roots and the Burns Park Loop.
Based on the flow from all of the normally small creeks in the Ozarks and throughout the Arkansas watershed, the high water will be with us for awhile.