Late next year, DDOT plans to perform a complete reconstruction of the two blocks of Florida Avenue between U Street and Barry Place. In addition to pedestrian, stormwater, traffic signal and utility improvements, the project will add bike lanes. Depending on how accurate a 2012 presentation on the area is, the design will include bike lanes on Vermont between Florida and V, bike boxes on Florida at Vermont, and and a combination of bike lanes and sharrowed lanes on Florida Avenue and Sherman. Combined with the work at Florida and 15th, it should lead to bike lanes on the entirety of Florida Avenue between 9th and 15th. Right now the project is awaiting ROW acquisition and won't go out to bid until June, with construction scheduled to start in October and end in May 2016.
DDOT has been planning to improve this part of Florida Avenue for over a decade now. A couple of plans, the 2004 Duke Plan and the 2007 Great Streets plan, had designs for this area which included among other things, reconnecting W and Bryant Streets and adding a traffic circle in at the intersection of Florida and Sherman Avenue. Those items do not appear to be a part of this reconstruction project. A more modest redesign was on the table in 2008, but that did not include bike lanes and it appears that the work was never done.
In 2011, DDOT presented 3 options for redesigning the area, which by 2012 they'd narrowed down to one. In the 2011 design, you can see that one option included bike lanes on Florida and on 9th, but those were later dropped.
One of the 2011 designs, via GreaterGreaterWashington (south is to the left)
The only image included in the Ward 1 update is for Green Infrastructure improvements, and doesn't show striping. But it does look similar to the 2012 plan, so it appears that much of the design will remain the same.
If the 2012 plan is followed, then 9th between U and V will have sharrows. Florida between V and Vermont will have southbound sharrows and northbound bike lane. Between Vermont and W, Florida will have a northbound bike lane and combination of a bike lane and sharrows in the southbound direction. None of these bike lanes will be next to parking, and the northbound section shown above will be separated from most traffic by a landscaped median (though parking and a traffic lane will also be east of the median too). North of W, the bike lane will be painted green to Sherman Avenue and placed between the turning lane and the thru traffic lane. The bike lane/sharrow combination will then continue to Barry Place. Bike lanes will also be added to Sherman between Florida and Barry Place.