Bjorn knows he will have to deal with the moment a long time. He knows he can't run away from the two shots he left in the bunker that cost him his first major championship.
Still, he refuses to let himself be defined by the big one that got away.
'I can't live in 2003,' Bjorn said. 'If I want to win a major championship I have to live now and I have to live in the future. And that's what I'm trying to do.'
Curtis was a remarkable story in his own right: No. 396 in the world ranking, a 500-1 long shot and the first player in 90 years to win a major championship in his first try.
But there is no escaping the image of Bjorn, hands on hip in utter disgust after watching not one, but two bunker shots barely reach the green and slowly roll back into the deep, sandy pit.
'It happens. It's a double bogey at the wrong time,' Bjorn said. 'And no matter how much I sit here and try to explain that, it could happen on the fourth hole in the first round and nobody could remember. That's just the way golf is.'
Unfortunately for Bjorn, it is just that. He had the field beaten through 69 holes, but they play 72, and trying to get it close on 16 instead of putting it 15 feet past the cup and taking his chances cost Bjorn a chance to win.
'When it happens to the guy that leads the golf tournament, then it becomes a big issue and it becomes a guy that's out there choking,' he said. 'It becomes the guy that can't handle anything or it becomes a big disaster.'
Despite his attempts at a positive attitude, Bjorn has had trouble moving on.
He hasn't won since, and despite two top five finishes to start the year, he is now 34th on the European Tour Order of Merit money list.
Bjorn is capable at Royal Troon, but his expectations are minimal.
Two weeks ago, his confidence was so shattered by a game in disarray that he walked off the course after six holes in the first round of the European tour event and withdrew, losing a battle with the demons in his head.
Bjorn stood on the tee and saw a fairway the size of a cart path, the hole the size of a thimble. He would have taken time off except for Loch Lomond, where he once won the Scottish Open, and the British Open, the most important major of the year, were next up.
Deciding to rely on the close circle of friends around him, and to return to coach Pete Cowen, he came back last week with a fresh perspective and contended through the front nine Sunday, finishing in a tie for 16th.
'I think obviously I would have liked to have been with better results coming in,' the Danish player said. 'I have no expectations for this week. I know that two weeks ago I was in a state where golf wasn't the greatest thing for me. So I can't go out with high expectations.'
Bjorn was playing behind Tiger Woods, who was four shots behind and seemingly had no chance as he finished the final four holes. Only when it was over - a double bogey-bogey-par finish for Bjorn - did it look like a close call.
If Woods only knew.
'We didn't think Thomas was going to do what he did,' Woods said. 'He was kind of running away with it.'
Unlike Bjorn, Woods is still a favorite this week, though he tees off Thursday in the unfamiliar position of not being the odds-on choice. That role goes to Ernie Els, who is listed by British oddsmakers at 7-1 to Woods' 8-1.
And then there's Colin Montgomerie, who is the big favorite - among the crowd, not the bookmakers.
This tournament means much more to the ruddy-faced Scot whose major championship failings haven't diminished the love his countrymen will no doubt show him when he tees off in his 15th British Open.
Montgomerie will begin each day walking to the course from his father's house a half-mile away, passing familiar sights on his way to a most familiar place.
He'll stick his tee into the ground he knows so well and hit shots on the same lines he mastered when he played Troon day after day after finally being allowed on the course at age 16.
Unlike 1997, when the crushing expectations were too much to bear and he shot 76 in the opening round, this time he's just happy to be here. British bookmakers make him an 80-1 pick to win, and even that may be generous.
'I thought back in June that I wasn't going to be playing at all, so it's a delight to be here in the first place,' Montgomerie said. 'And I will do my utmost to do as well as I can.'
Montgomerie is still dealing with his much-publicized divorce. Often criticized for being dour and glum, Monty had reasons this time to walk around with the familiar pout on his face.
But things took a turn for the better when he survived a 12-man playoff in Sunningdale, England, to earn a trip back to his home course for the Open. He didn't make it by much, but he avoided being out of the Open for the first time since 1989, when he failed to qualify for the Open at Troon.
'I wouldn't say I'm at a peak, but at the same time I'm a lot better than I was,' Montgomerie said. 'I think time is a healer and you get on with things and that's what I've got to do.'