Billing signed from Huddersfield Town this summer and has been ever present for the Cherries in the Premier League.
Howe is impressed by what he has seen from the Danish central midfielder.
He told the Daily Echo: "He's made a very good start, Phil. We're very pleased with him.
"He's come in and had a real impact on the group and on the team. He's trained well and played well. I know we're very early stages, but it's been a promising opening for him.
"I think he did come here short of fitness, probably understandably as his pre-season was very mixed and difficult for him but he's got up to speed very quickly.
"He's done a lot of hard work in a short period of time.
"I know there's a lot more to come from him physically and with every aspect of his game, so we look forward to continuing that journey with him."