Jason . . . there is a very big difference between "slow release" fertilizers (organic fertilizer, generally) and "timed release" fertilizers. Slow release fertilizers release their chemicals as part of a natural chemical breakdown of the fertilizer constituents. Time-release fertilizers are held in little manufactured, ball-like capsules that pop open when temperature and humidity hit some kind of a target -- some earlier and some later -- but the stuff inside those little balls is plain old chemical fertilizer that is available to the tree immediately it is released and passes through bonsai soil rapidly -- like Miracle Gro.
Brian, our trees do not care whether they get organic fertilizer or so-called "chemical" fertilizer. (ALL fertilizers are made up of "chemicals", BTW). It's only how easily and quickly the stuff is available that is the difference between them -- all the mythos attached to "organic" notwithstanding.
Which you might want to use depends to some extent on the soil you use for your trees. If you use a 100% inorganic mixture (Turface and granite, for instance) "organic might be the way to go. The more organic material you have in your soil the better off you might be with an inorganic fertilizer. That has to do with how the molecules pass through the soil. Organic fertilizers tend to adhere to the inorganic soil, while inorganic fertilizers will tend to pass right through. If you have organic materials in your soil, the inorganic fertilizers tend to adhere to the organic particles and will stick around for a bit.
As an aside, many "organic" fertilizers do not have the micronutrients trees need.
But it's all pretty much a moot point, anyway, because we water so often that we flush the pots at least once a day and it's by-by fertilizer -- no matter what you use.
Poo balls are unsightly, often smelly, and unpredictable. They don't supply your tree with measured amounts of the chemicals the tree needs -- including micronutrients. They are an anachronistic holdover to ancient Japanese practices, but horticultural science has passed them by. They're the buggy whips of the plant nutrition world.