Bedoya grabbed the only goal of Wednesday's game in the 39th minute as the USA prevailed in their first outing since exiting the 2014 World Cup to Belgium at the last 16 stage.
US coach Jurgen Klinsmann selected a young and largely European-based squad for the team's maiden appearance on Czech Republic soil.
Joe Gyau, Greg Garza and Emerson Hyndman made their international debuts, while Julian Green earned his first start.
However, it was Bedoya, one of the players to represent the USA in Brazil, who had the decisive impact against a Czech outfit that failed to qualify for the global showpiece.
Darida came close to giving Czech Republic the lead from Tomas Rosicky's cross at the end of a swift first-half break.
Yet the Freiburg midfielder was at fault soon after and the visitors took full advantage. Darida was dispossessed after receiving the ball from Petr Cech and although the goalkeeper saved Mix Diskerud's subsequent strike, Bedoya was on hand to convert the rebound.
Seeking a morale boost ahead of their Euro 2016 qualifying campaign, which begins on Tuesday with a home game against the Netherlands, Czech Republic upped their game after the interval.
US back-up goalkeeper Nick Rimando, who replaced Brad Guzan following the interval, was forced to make a number of saves to preserve his side's lead.
Despite late pressure from the hosts, the Americans were able to hold on and give Klinsmann something to build on as his team begins a new cycle.
The US are back in action next month, with Ecuador and Honduras set to provide friendly opposition in Connecticut and Florida respectively.
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