The 31-year-old striker, on loan from Manchester City, is expected to play some part for the Bluebirds at home against Bristol City on Saturday.
"We're trying to manage it properly from mistakes that have happened to him before," Jones said.
"He's not injured, there's not a problem, he has a programme and that's what we will stick to.
"Let us get on with what we think is right here. We're doing it for the benefit of not just the club and the national team, but for the player himself.
"I spoke to [Wales caretaker-manager] Brian Flynn and everything was fine, not a problem, but... everybody thinks they have a little bit of knowledge and they should know best.
"Every international team is entitled to pull a player in, injured or not, and run the rule over them.
"We were on the doorstep, so he hasn't got to travel anywhere except the 100 yards up the road into the hotel or they walk 100 yards down.
"Nothing has been hidden, there's no hidden agenda whatsoever. It was in the interest of Craig Bellamy and not for Wales and not for this football club.
"Craig wants to prolong his playing career for a long, long time."
As well as the expected availability of Bellamy, Jones has fellow forward Michael Chopra back in the squad after an ankle injury.
But defender Darcy Blake is suspended, defender Paul Quinn is out with knee ligament damage, while midfielder Danny Drinkwater is back with parent club Manchester United being treated - although he should be back with Cardiff next week.
Source: BBC Sport
Source: BBC Sport