The game was called after nine innings because both teams ran out of pitchers.
Bedard allowed five hits, walked two and struck out two. He's set to start on Thursday when the Pirates host Philadelphia.
The Orioles took a 4-1 lead in the fourth on consecutive home runs by Ronny Paulino and Jai Miller. Paulino's homer, his first of the spring, was a three-run shot.
Orioles starter Jake Arietta went five innings and gave up six runs and eight hits. He struck out five.
Garrett Jones hit a two-run homer and Alex Presley added a solo shot for Pittsburgh.