MLB.com's No. 20 prospect allowed one run on two hits over six innings Wednesday as the Class A South Bend Silver Hawks shut down the Fort Wayne TinCaps, 3-1.
Bradley walked three batters and struck out seven in earning his first professional victory.
"I'm getting better every time. I'm figuring things out each time I take the mound," he said. "I know it's a cliche, but it's all about throwing strikes. I don't mean to sound cocky, but I know I have the stuff to get people out."
Bradley came out of the gates slowly, surrendering a first-inning run as the TinCaps played small ball. Jace Peterson drew a leadoff walk, stole second, advanced to third on a sacrifice bunt and scored on Travis Whitemore's sacrifice fly.
"I just wasn't dialed in to pitch," Bradley admitted. "I walked two people in that first inning, which I don't usually do. I was just thinking about too many things. I felt fine in my bullpen and I was spotting up and throwing good pitches. Now I just have to translate that to the mound."
Once the 19-year-old right-hander got to the dugout and took a moment to regroup, he found his groove and cruised through his final five innings. He retired eight straight batters before allowing a two-out single in the fourth to Duanel Jones, who was thrown out trying to steal second by catcher Roidany Aguila.
Bradley worked around Corey Adamson's two-out walk in the fifth and, after striking out the first two batters in the sixth, he got some more help from his defense. Right fielder Chris Ellison threw out Casey McElroy trying to stretch a single into a double.
"They were huge," Bradley said of his teammates. "Anytime you give up an early run, the defense plays a huge part getting you back into the game.
"After that first inning, I regrouped and got my thoughts together. Once I got back in the zone, I was OK. My curveball was working and I was able to spot my fastball. I knew coming into the game they had seen me pitch and that they were likely going to be sitting on my fastball early, so that's why I started maybe every other batter with an off-speed pitch to keep them honest."
Bradley's curveball comes at hitters in the mid-80s and complements a fastball that sits around 95 mph. But the Oklahoma native realizes that adding a changeup to his repertoire may be the biggest thing standing in the way of progressing through the D-backs system.
"My curve is my out pitch, but anytime you can throw hard you have to use that," said Bradley, who was selected seventh overall in last year's Draft. "The problem is that if you only throw two pitches, they can let the curveball go and sit on the fastball. Once you add a changeup to the mix you keep them guessing, and that obviously helps you.
"I threw my changeup a lot during instructs and in Spring Training. Now I have to use it more consistently and throw it where I want it."
In his season debut last week, Bradley allowed a run on four hits and a walk while striking out seven over five innings. Against Fort Wayne, he went an inning deeper before turning things over to his bullpen, which has not allowed a run over its last 18 1/3 innings.
TinCaps starter Frank Garces yielded one run on two hits while striking out six over five innings and did not factor in the decision. Michael Kelly (0-1) gave up a pair of runs on three hits and a walk in one inning.