What kind of abilities reveals you on the brush?
Is it all abilities? On hit abilities? Skillshots? This is probably one of the hardest to find out, since one is always on the other side.
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I don't understand fully what you ask for but I'll try to give a general explanation.
Some abilities give vision to an area upon cast. Such as Lux's E, Leona's R and Syndra's W (landing). These abilities give vision to the area only - not you in particular. If you are in that area (say a bush) then you will be temporarily spotted.
Other abilities have distinctive things that happen when they hit. For example Ezreal gains stacks of his passive if he hits. Morgana has a very obvious sound for her binding and her passive heals her if hit. These abilities do not give any vision of the area and you cannot be seen. The player uses indicators to deduce you are in the area.
Other abilities grant vision upon hitting you such as Diana's Q. These abilities will reveal you only, not the area if you are hit granting vision for the enemy.
If you are in a bush:
Auto attacks reveal you.
Spell casts DO NOT reveal you but reveal the spell animation. For example if Caitlyn fires her Q the Q animation will be seen coming OUT of the bush but not while it is in the bush. You are not revealed.
Some spells like Rumble's flames DO NOT show at all if you are in a bush. Rumble can stand in a bush, cast his skill and damage people and they cannot see what is happening at all.
If I go into a bush as Yasuo and usebmy Q and stab outside the bush, does my opponent see the attack?
Soraka's Q kinda reveals invisible Teemo 
Little known tidbit 
s W can Also be used to scout bushes as you can only activate it when a champ is around.
If an attack skill that is not a skillshot is used while in the brush, the champion using that skill will be revealed for a short time. Your champion will also be revealed when you auto-attack from within a brush. If an ally attacks from a brush, you will also be seen.