Like the Frederick Douglas Bridge, the 11th Street Bridges (one of which is officially the Officer Kevin J. Welsh Memorial Bridge) are also being redesigned with an eye on replacing it. Unlike the Douglas, the 11th Streets' Final EIS is already complete. For more on it you can go here, and for a statement against it check out the Sierra Club.
Again, let's ignore the existing bridge and focus on the planned one.
It's hard to say when this bridge might be replaced but it "would cost $465 million and take about five years to complete." The preferred alternative will basically include two bike lanes, one on the upstream side of the local traffic lanes and one on the downstream side. This is the equivalent of creating two bridges. The preferred alternative will consist of two bike bridges starting at 11th and N on the north. The downstream bridge will connect to Good Hope Road in Anacostia Park, with a connection to MLK avenue at U Street. The upstream bridge will connect to 13th and U St SE. Below is the cross section of the chosen bridge. See a map here.
So what does the new bridge - if it's built - need to make cyclists happier?
1) On the west side downstream, a quicker connection to the ART. Right now users have to go two blocks past the Navy Yard ART trail. That seems too far. A ramp from there along the outside of the bridge up to the trail seems a simple solution.
2) On the west side upstream, a quicker connection to Water Street and thus the ART. As planned users would have to go a block out of the way - admittedly not the end of the world, but also pretty easy to fix since the trail would be at ground level here.
3) Connections to the Shepherd Industrial Spur (a future bike trail we're told) from MLK Avenue and from the 13th Street ramp.
4) On the east side, a connection from the upstream lane to Anacostia Drive SE. Right now there appears to be no connection to this span from the ART.
None of these are undoable (unlike the idea of keeping the old Douglas Bridge as public space, what is that guy on?), throw in some nice wide lanes, lighting, signage and you've got yourself a nice little bridge.