Bidwell made the comments on Monday during an appearance on the Doug and Wolf show on 98.7 Arizona's Sports Station.
The Cardinals have the No. 1 overall pick in the draft after a 3-13 campaign in 2018. The team hired Kliff Kingsbury in January after firing first-year head coach Steve Wilks. Kingsbury briefly coached Murray at Texas Tech.
Bidwell said it's great to have new players and new excitement around the game and it causes speculation and talk. He also complimented Cardinals rookie quarterback Josh Rosen, who was selected with the No. 10 overall pick in the 2018 NFL Draft.
"Josh is a smart guy, he's been around and he's seen what happens year in and year out," Bidwill said. "There's always a lot of speculation that turns out to not be true. But moving forward, we're going to continue to build this team and build around the foundation that we have."
Some of the hottest fuel for the speculation came from Kingsbury himself, who said in October that he would pick Murray with the No. 1 overall pick in the NFL Draft if he could. That was obviously before he was in the position to do exactly that.
Murray worked under Kingsbury during the Aggies' 2015 season. He later transferred to Oklahoma and went on to win the 2018 Heisman Trophy. The first-round MLB Draft pick is also expected to be picked in the first round of the 2019 NFL Draft on Thursday, April 25 in Nashville, Tenn.
Most mock drafts have the Cardinals selected Ohio State defensive end Nick Bosa with the No. 1 overall pick.