Bridenstine said successful development of the capsule was key to achieving NASA's top priority - the resumed "launching of American astronauts on American rockets from American soil" for the first time since the space shuttle program ended in 2011.
SpaceX CEO Elon Musk recently announced that a key Crew Dragon safety test could take place as early as November.
NASA and SpaceX had previously aimed to launch the Crew Dragon on an initial test flight carrying two astronauts to the International Space Station in 2019.
Mr Bridenstine said: "It's time to deliver".
"Human space flight is the reason SpaceX was created and we are honored to partner with NASA to make this happen", Musk said.
"We are not going to take any undue risk", Bridenstine said, standing beside Musk outside a clean room that contained a Crew Dragon capsule.
But he also emphasized NASA's concern for astronaut safety, saying the timeline could slip.
Musk said overcoming problems with re-entry parachutes had proved especially challenging.
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Bridenstine informed reporters on Thursday high-altitude abort check of a system created to propel the capsule to security within the occasion of an emergency on the way in which to orbit would occur in "short order", although he didn't present a particular date.
Other testing includes 10 additional mid-air "drop tests" to test parachute resilience and performance, Bridenstine said.
SpaceX efficiently launched an unpiloted Crew Dragon in March to the Worldwide Area Station, a $100 billion orbital analysis laboratory that flies about 250 miles (400 km) above Earth.
Musk said during the press conference that the newest design of the parachutes, which he referred to as Mark 3 parachutes, are 10 times safer than Mark 2 parachutes and are twice as safe as Apollo's parachutes.
Responding to questions on Twitter, Mr Musk replied: "For what it's worth, the SpaceX schedule, which I've just reviewed in depth, shows Falcon & Dragon at the Cape & all testing done in ~10 weeks".
Under that time frame, the first Starliner manned mission is all but certain to slip into 2020.
Since retiring its space shuttle program, NASA has had to rely on Russian Federation to ferry astronauts to and from the space station at a cost of $85 million a seat.
Whereas Musk and Bridenstine equipped few concrete well-known aspects on their joint investigation into an explosion at some stage in a capsule ground sign in April, Musk mentioned incidents had been inevitable at some stage in complex pattern processes and rigorous attempting out.
The tour follows a public spat days earlier between Musk and the NASA chief, who bristled at Musk on Twitter for celebrating an unrelated milestone achieved on SpaceX's deep-space Starship rocket while completion of the Crew Dragon project remained delayed.
Bridenstine said the agency was "still buying seats" for ride-alongs aboard Russia's Soyuz as an "insurance policy" against future delays in US crew capsule development.