his diet should consist mainly of turtle pellets.
i used to give my red-eared slider small bits of raw hamburger meat as a treat. they will eat almost anything you throw into the water though. don't dump it in all at once or the water will get filthy really fast. and don't feed him too much.
if you feed him at the same time every day he'll remember and come to expect it, probably bang on the glass or try to climb up it.
oh, and get him a proper terrarium, ditch the fish bowl. turtles are not fish, they need to have a landing where they can climb up out of the water and bask (preferably under a heat lamp). if they are just swimming all the time they can get really tired and, believe it or not, drown.
just get a 10 gallon tank and put a shelf in it, fill water up to the level of the shelf so he can climb onto it and get one of the clip-on heat lamps to clip to the side of the terrarium. whole setup is dirt cheap and will keep the turtle happy. if you want to go all out like i did you can get a filter for the water. you will have to change the water a hell of a lot less.
also removing the chlorine from the water isn't necessary with turtles like it is with fish but i'd recommend doing it anyway. chlorine is an irritant and a bottle of chlorine remover is cheap, you only need a tiny capful for 10 gallons and the turtle will be more comfortable.
hope this helps