Bradley and Schultz were late cuts from the roster this spring and have yet to open their Minor League campaigns.
Bolsinger, who was a non-roster invite to spring camp, has made one start this year and tossed 6 2/3 scoreless innings.
"I've always liked him," Towers said of Bolsinger. "I know nobody talks about him, but every time I've seen him -- in Double-A or Triple-A -- I've seen him probably five or six times, and I've never seen a bad start. He just stays off the barrel. We told him that when we sent him down, you never hear his name, nobody writes about him, but we know what you're doing and you're on our radar screen."
The D-backs also have relief options at Double-A Mobile in Jake Barrett and Matt Stites, who were both in big league camp this spring.
The bullpen has struggled this year, but Towers said it was too soon to be thinking about making any changes there.
"I think we're just trying to get guys in slots," he said, referring to set roles. "We'll stick with what we have. What would really help is if we get a starter who goes six or seven innings a couple of days in a row."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.