McDonough confirmed the comment on Sunday to AZCentral.com but declined to elaborate. The NBA had not announced the fine as of Monday afternoon.
Bledsoe later tried to put that tweet in context, although McDonough wasn't buying the excuse.
"He said he was at a hair salon. ... I didn't believe that to be true," McDonough said last month. "He won't be with us going forward."
Suns veteran forward Jared Dudley told AZCentral.com that he understands the NBA's position.
"The league doesn't want to set a precedent of players going off on social media," Dudley said. "If you ask (Bledsoe), he probably regrets doing that. He probably would have done something in a different manner.
"I just think in general you can't even demand a trade when you're doing interviews. Just keep it more in house."
Bledsoe is averaging 15.7 points, 2.3 rebounds and 3.0 assists in three games for the Suns this season -- his fifth with the team. He is entering his eighth NBA season and owns career averages of 13.1 points, 3.8 rebounds and 4.6 assists.