I use shredded/chipped beech tree as a bedding. It's pretty much free of dust and I like the smell of it. It's safe for tiels and my tiel loves exploring the bottom of his cage, looking for dropped seeds or just messing around.
I don't know how well available it is in the US, but over here every pet store sells it, and it's pretty inexpensive. I usually just scoop out the areas where Puck poops most often whenever necessary. I clean the entire tray about once every two weeks, sometimes earlier and sometimes later.