Ruddy has shone for the Canaries in their rise to the top-flight and has become a regular in Roy Hodgson's England squad, but now faces three months on the sidelines with a thigh injury.
The absence of the 26-year-old will see summer signing Bunn get an extended run in the first team, with the former Blackburn man helping the team to a 1-1 draw at Southampton on Wednesday night.
Midfielder Snodgrass, who scored the Canaries' equaliser at St Mary's, said: "We'll miss John. What he brings to the team is clean sheets.
"But we've got a great keeper in Mark Bunn, who is terrific. I think you saw that in the Tottenham Hotspur game and against Southampton.
"He was calm, composed and pulled off some good saves, but I would like to wish John a speedy recovery because he is a great chap and great keeper.
"His return will only bolster the team."
Ruddy has been one of Norwich's standout players this campaign, but they continued their fine run without him against Southampton, extending their unbeaten streak to eight games in all competitions.
Snodgrass was involved in both goals at St Mary's, first giving away the free-kick from which Rickie Lambert gave Southampton a 32nd-minute lead.
City players felt aggrieved after the striker handled in the build-up but soon equalised as Snodgrass won a free-kick on the edge of the box and then beat goalkeeper Paulo Gazzaniga at his near post to level things up.
"I fancied my chances," Snodgrass said. "I scored a few free-kicks for Leeds when I was there.
"It went in and people will blame the keeper, but you've got to get it on target and I've done that. We showed great spirit and character to come back and I think there was only going to be one team that was going to win it in the second half.
"The first half wasn't good enough but we take away a point and firmly believe we could have won the game.
"It was a wee bit unfortunate that Holty (Grant Holt) failed with a header and a couple of half-chances. Pilky (Anthony Pilkington) had a half-chance as well and if they go in then we win the game.
"Sometimes you get them but sometimes you're a wee bit unfortunate, but we will pick ourselves up and look forward to the weekend and what will be a tough game with Sunderland.
"We're back at home, which seems to be a place where we're winning these days, so we're looking forward to it."