Hamilton rode a black Yamaha YZF-R1 bike alongside works riders van der Mark and Alex Lowes earlier this month, the track test overseen by the Crescent team that operates Yamaha's WSBK outfit.
“Lewis already did two track days on his bike [before] and the people of his team were a little bit concerned because of his speed,” van der Mark told Motorsport.com.
“He was very fast but he didn’t have a riding style. He had lots of lean angle, so the initiative came a bit from his team that he'd get a few tips from professionals.”
The five-time F1 champion, who had a track outing alongside LCR Honda MotoGP rider Cal Crutchlow earlier in the year, suffered a small crash at Jerez, escaping it without injuries.
“During the first day I was alone with Lewis and on the second day my teammate Alex Lowes joined us,” van der Mark continued.
“On the first day I’ve was only trying to make him go a bit slower. I had to stop him, he’s not afraid at all and he tried to take corners as fast as with his car.
“During the second day we worked a lot on his style.”
Van der Mark said he was an admirer of Hamilton's, and described the experience of working with him as “very cool” and “a pleasure”.
“Even if it’s just for fun, he was so motivated to learn,” van der Mark said. “He asked loads of things and that was special to see.
“You see it’s fun for him, but he goes all the way. He wants to do it right and wanted to learn as much as possible.”
However, the Dutch rider – who finished third in this year's World Superbikes standings – was reluctant to estimate how competitive Hamilton could get if he took up bike racing on a full-time basis.
“You see he’s not afraid at all. You also see that he doesn’t have any doubt, you see a lot of riders who have a little doubt, but he’s going all the way if he decides to do it that way.
“That’s the same in a car, that’s just his natural talent. He can ride a bike for sure - I don’t know how much faster he can go.
“I know he can be much faster but it’s difficult to predict what he could do on a bike.
“He has only ridden four days now and he was about seven seconds slower than us. With that he’s faster than most other track day riders.
“You can see he has a special talent, but I don’t know if he wants to do that [full-time].”
Quotes translated by Mark Bremer