As you can see above, while there is a strong concentration of Cherry Blossoms at the Tidal Basin, otherwise the blossoms are very spread out. Washington DC is a great biking city, having just been awarded Gold Bicycle Friendly Community status by the League of American Bicyclists - the only major East Coast city to receive this designation.
Capital Bikeshare
Capital Bikeshare is the established, docked bike sharing program in Washington DC. It is a great way to get around Washington DC, and perfect for seeing the Cherry Blossoms as there are multiple stations where there are Cherry Blossoms to include the Tidal Basin, East Potomac Park, the Mall, Georgetown, the National Arboretum; there are also hundreds of others stations in and around the city.
You can rent a single bike for 30 minutes for $2, but the better deals are $8 for a 24-hour pass, or the $17 for a 3-day pass; both come with unlimited free 30 minute rides. Beware - if you go above 30 minutes on a single ride (without getting an extension at a full dock), they will start charging you. However, you can have as many free back-to-back 30 minute rides in your time period as you would like.
For more information on Capital Bikeshare, please see their website. Also, be sure to download the app so that you can know where there are stations and how many bikes and/or docks they currently have.
Dockless bikeshare
Dockless bikeshare is a new concept in Washington DC; it began late in 2017 as a trial, and a number of companies can have up to 400 bikes in the city. The companies include Jump DC, Spin, OFO, LimeBike, and Mobike. It's another great option, but it's good to be flexible, with limited bikes, you may need to switch between companies.
Seriously don't try to drive and park at the Tidal Basin