It was in the middle of the afternoon at a section between the London Road roundabout and the A157 roundabout.
Teresa and John Gillson, 59 and 61, from Wigston, near Leicester, said he was wearing a jacket, trousers and a cloth cap that looked to be from the turn of the century.
They said the bicycle also looked as though it was from the same period.
Mrs Gillson said: "We both saw it at the same time. It was really, really strange."
"We've never forgotten about it."
"We said, look at that idiot cycling in the middle of the road – and then it was gone."
They saw the cyclist at the crest of a hill where the bypass is bordered by a steep embankment on both sides.
He was a short distance in front of them but when they drove closer he vanished.
Mrs Gillson said there was nowhere for him to have left the road.
The couple regularly holiday at their caravan in Mablethorpe.
They were driving home when they saw the mysterious cyclist a couple of years ago.
Mrs Gillson said: "It's something that's always bugged us because there is no explanation."
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