Beal, who missed the Wizards' 125-124 loss to the Atlanta Hawks on Monday, responded to the jab during the Warriors' game versus the Utah Jazz.
Bazemore responded to Beal's tweets following Golden State's 119-116 win.
"I guess you can't joke anymore," he said. "I feel like I'm a pretty lighthearted guy."
"My loyalty is to (Steph Curry). It kind of got out of hand. I didn't check my phone all day until after the game," he added. "It's kind of blowing up, but I don't get involved in that crap."
Beal, who will miss Washington's upcoming game against the Hawks on Wednesday, is averaging 31.4 points this season, second only to Curry.