The American leader has form for grabbing hands and holding on to them for a long period of time, but the Queen was spared this.
James said: "Donald Trump is more inhibited when he's shaking hands with the Queen. He was leaning forward from a distance, with a tentative pawing of her hand.
"The Queen only ever offers her fingertips so he couldn't get a grasp. He probably wasn't touching much more than her fingers.
"Because he's got such huge hands, it probably does look like a fist bump."
She added: "It's hilarious - watching the size differentiation between them is comedy gold.
"His huge hand was enveloping her tiny one. But she was quite happy, chuckling and laughing.'
The monarchy's official website has some simple advice on how to greet the Queen.
It declares of those who decide not to bow or curtsy: "Other people prefer simply to shake hands in the usual way."
Trump has been described as approaching a handshake like an arm wrestle, in which he clasps the hand and pulls sharply, leaving the recipient off-balance.
He yanked French President Emmanuel Macron's hand at the Bastille Day celebration in July 2017, holding on to it for nearly 30 seconds.
At the White House in April 2018, he also led the French leader away from reporters after shaking his hand and keeping hold of it.
Meanwhile, the Duchess of Cornwall has been caught on camera delivering a cheeky wink to officials who had just met the President as part of his state visit to the UK.
The President and Melania Trump joined Charles and Camilla at their home at Clarence House for tea on Monday.
After the private meeting, all four posed in a room for photographs and Trump met further members of the royal entourage.
As they were leaving the room, the Duchess winked cheekily at the men who had just shaken hands with the President.
The gesture was broadcast on Sky News and noticed by royal watchers, who joked it could be code for the Secret Service.
The official visit began with a royal welcome at Buckingham Palace where Charles and Camilla met Trump and Melania as they landed on Marine One.