The Centennial Bridge between Davenport and Rock Island has a wide walkway on the east side and is quite attractive. (The west side walkway has been cut on the Illinois side)
The Cassville Ferry is the only ferry on this stretch - variable hours.
Most bridges - except Interstate - permit bicycles, although many are narrow and dangerous. Generally, any bridge completed before 1970 is going to be pretty narrow unless it was built with a sidewalk. The Arsenal Bridge in Rock Island is also doable, the bridges at Clinton and at Savanna are scary. Both bridges in Dubuque have sidewalks/shoulders, but the US 61 bridge is more expressway with trickier exit access. The US 18 bridge has wide shoulders and moderate traffic - the Blackhawk Bridge, Hwy 9, is narrow and scary. At La Crosse, the new eastbound US 14 bridge - Cameron Ave - has the bike lane.