The Raiders acquired Bryant from the Pittsburgh Steelers in April in exchange for a third-round pick of the 2018 NFL Draft.
"He's got to get out here and play better," Gruden said Saturday, via the Las Vegas Review-Journal. "He's in a competitive situation. Right now, a lot of the other receivers have had a nice camp.
"He's just got to learn the offense. He's got to stay out here. He's had some illnesses. He's got to get on the field. He's got to master the offense and become more versatile, and that's the key to making this team better."
Bryant is expected to be an integral part of Oakland's wide receiving corps that includes Amari Cooper as well as free-agent signee Jordy Nelson.
"I'm not saying he's behind," Gruden said. "I'm saying he's got to be more versatile. I'm not going to say any more than that. He's in a competitive situation. Nothing is going to be given to anybody. It doesn't matter how you got here or what your history card says, we need everybody to understand the best players are going to play. He's got to be more consistent, and I'm confident he will."
Bryant was suspended for the entire 2016 season due to multiple violations of the league's policy on substance abuse.
The 6-foot-4, 211-pound Bryant returned from his year-long banishment and tied a career high with 50 receptions for 603 yards and three touchdowns in 15 games with the Steelers.
A fourth-round pick out of Clemson in the 2014 draft, Bryant scored eight touchdowns on only 26 receptions as a rookie, averaging an eye-popping 21.1 yards per catch.
Bryant followed that up by hauling in 50 receptions for 765 yards and six scores during his sophomore campaign.