The rookie stopper stepped in for injured number one Shwan Jalal and found his feet by keeping a clean sheet in the 2-0 victory over Yeovil Town.
He is set for his second start of the season when Cherries visit Bristol Rovers tomorrow and Moss believes the 6ft 4in Londoner is showing the right approach as he bids to prove himself.
Moss said that Stewart's desire to keep out the Glovers led to the pair coming in on their day off to prepare.
He badgered me all the way home from Leyton Orient to come in on the Sunday, so we did an hour-and-a-half of training on the Sunday morning and he had a great session, Moss told the Echo.
He then had a really good session on the Monday and it was all positive because it left me in no doubt that he was going to put in a good performance for us on the Tuesday night, which he did.
His preparation was top notch and if your preparation is right, nine times out of 10 your performance will be right.
Moss admitted coming off the bench at Orient to replace the injured Jalal was not the ideal way for Stewart to make his Cherries bow, with a substitute role particularly difficult for goalkeepers.
But he was pleased to see his protégé earn a shut out in the success against Yeovil.
The ex-Cherries keeper added: I thought the boys produced a professional performance against Yeovil and Jon certainly played his part in that by making two or three good saves and distributing the ball well when he had to.
It was a great start for him because he will be in our goal while Jal recovers from his injury.
It's a good amount of time for Jon because it will give him an opportunity to stake his claim. He knows that Jal will be absolutely desperate to get straight back in the team and it will be a good fight between the two of them.
Jalal, a key man during Cherries' relegation escape and promotion campaign, is on the sidelines after sustaining a fractured eye socket.