From the U-Dub, you can head north on the Burke-Gillman trail. In Bothell it becomes the Sammamish River trail which you can take to Redmond where you can catch the 520 trail back into Bellevue.

If you want a long gravel ride, take the Sammamish Trail (paved), at Marymoor Park look for the Marymoor Connector Trail (paved) and take that to the East Lake Sammamish Trail (mostly gravel), in Issaquah find the Issaquah-Preston trail (gravel) which becomes the Preston-Snoqualmie trail (gravel), turn left onto the Preston-Fall City Rd, cross the river in Fall City, go right on 203 and then left onto 356th and climb up and take a right onto the Snoqualmie Valley Trail (gravel). Follow that trail (with a short road detour in the Snoqualmie Falls area) up to Rattlesnake Lake where you'll catch the Iron Horse Trail (gravel) that will take you over Snoqualmie Pass (bring alight for the 2+mile tunnel you'll ride through) and ultimately across the state to the Idaho Boarder if you are really want to push things :-)