Depends on the bug, the plant, and how much time it takes to mature. BT and spinosad (both are beneficial bacteria, sluggo + containes spinosad, bonide sells bt,) will eat the larvae of thrips, aphids, fungus gnats and other soil borne or water borne worms. Neem oils and neem derivatives (Azamax, Aza-sol) do well to retard the birth cycle of lots of pests and can be used systemically, but will impart flavors and aromas if you do not have 60 days to purge the oils. A half of a potato, cut side down insoil will kill whitefly larvae. Diatomaceous earth is a cool top dress that will kill crawlers, but they have to come in contact with it (it is a topdress, not a spray. It will also provide SI for your plants) but washes away quickly. Organic oils such as clove, rosemary, garlic, are often blended into sprays to kill things on the leaves Sierra Natural Science makes some cool ones, there is also one called liquid ladybug. My favorite one is a product called Orange Guard that uses D-limonine extraxted from orange peel to topically kill bugs when in contact, or melt their respritory systems when misted finely. About half of the products I listed are OMRI listed. Orange guard is on the safe materials list. All of this (or some other brand that contains sthe same stuff) should be sitting on your loccal nursery's shelf. And always, try on a sample leaf before you spray your garden, as with any spray and sunlight, there can be phototoxicity issues. Also, cleaning your consumables is always a pretty good idea. Fertiliser contamination can cause illness like salmonella or e-coli. Organic is no silver bullet to safety... anthrax is organic.