They return as two of the brightest prospects in European golf -- Wallace a three-times winner on the European Tour last year while Bjerregaard won the Dunhill Links at St. Andrews.
Wallace has an intense demeanour on course somewhat reminiscent of compatriot Ian Poulter, something that can be seen in a photo he posted on Twitter at the Arnold Palmer Invitational last Sunday.
In contention until he bogeyed the penultimate hole, the photo shows him with his raised hands holding a fence and his head bowed as the dejection that he could not win sank in.
"That was on the back of the 18th tee," Wallace said in a telephone interview with Reuters on Wednesday.
"It is a different photo (from the upbeat stuff many put on social media). The reason to (post it) was to show I was gutted I couldn't win the tournament, or have a chance.
"As soon as I saw the picture, (I thought) this is posting a different side. This is the anguish players sometimes go through."
Wallace finished bogey, bogey to tie for sixth, a result that showed his game is trending going into the PGA Tour's flagship event.
The world number 35 will carry a five-wood this week, a club he thinks will come in useful on several holes, including the par-five second, where he used it for both his tee shot and second shot in a practice round early on Wednesday.
There has been some chatter that the course will yield plenty of low scores, due to a combination of little rough and soft conditions after recent rains.
Wallace begs to differ.
"I think it will change a little bit come tomorrow," he said, predicting the greens will have dried out considerably by then.
"I played late yesterday and early this morning. The wind was up at 7.30 this morning. It’s playing long."
Wallace and Bjerregaard will also make their Masters debuts next month.
Wallace has never been to Augusta National, but teased that he has something "special" lined up for his first practice round there scheduled for the Sunday before the tournament.
Bjerregaard visited in February, and says he particularly enjoyed the sweeping view from the clubhouse.
Bjerregaard has not played much this year, instead busy moving from London to Monaco. "My fiancée has family there and a few friends," he said. "In the UK we didn’t have that many friends nearby."
He is ready now for a stretch of golf. "You never know," he said of his chances this week.
(Reporting by Andrew Both in Cary, North Carolina; editing by John Stonestreet)
