The National Park Service is investigating the replacement of the current vehicle security barriers - a line of jersey walls installed in 2001 - with a permanent barrier that creates better access and is more aestheically pleasing. Last month they released the Environmental Assessment for the project. While it won't fix the awful approach to the 14th Street Bridge, it should improve the ride along the path beast East Basin Drive.
As the NPS writes
Bicycle commuters frequently travel the route along East Basin Drive to and from 14th Street Bridge, sharing the sidewalks with pedestrians along both the perimeter of the site and the internal paths inside of the barriers.
There are 3 alternatives (not counting the no build) - and they mainly change where the new security barrier would go. For all of them NPS writes
Paths would be constructed inside the barrier, with alignments that reflect Olmsted’s design intent and the sidewalk would be widened along East Basin Drive to help in separating pedestrians visiting the Memorial from cyclists traveling through the area.
In alternative 1, the preferred alternative, the sidewalk would be widened to 12 feet wide along East Basin Drive, and a pedestrian plaza would be created at the inlet and outlet bridges where users can decide whether to enter the site along the Tidal Basin path, or continue along the sidewalk. One option would be to split the sidewalk at the south lawn with the barrier, reserving the Memorial side for pedestrians and the road side for cyclists. Some paths on the east frontage would be 10' and allow cyclists.
Map of Alternative 1
Alternative 2 would be similar to 1 for cyclists but the barrier would be farther away, which might be more pleasant - and one could argue safer.
The text says there will be a 12 foot sidewalk along East Basin Drive, but the picture calls it a 10-foot Bicycle Path, so that's confusing, but wider is probably better - since pedestrians will use it no matter what you call it.
Alternative 3 moves the barrier further in and makes it semi-circle shaped, but for cyclists it's basically the same.
So there's not much of a difference for cyclists, but I suppose I prefer Alternative 2 or 3 because it gives cyclists more room in case of a hazard and it will probably be nicer. Moving the wall away will likely let snow melt faster and make the path cooler in the summer too.
There is one other bike element of note.
There is a Capital Bikeshare Station located on the south side of East Basin Drive across from the Memorial. This Bikeshare station will be relocated in the future; however the final location of the station has not yet been determined.
Also, did you know that the Plaza along the Tidal Basin was originally part of a road that led around the Jefferson Memorial so that people could drive around it? That was removed in 1970 as an opening salvo in the War on Cars. Nixon!