When I am playing Support in bottom lane vs. Caitlyn (plus her Support) and she keeps putting her Traps in the brush, how do I react to that? Should I try to take them out in a safe second (by walking over them) or, is it better to just leave them there? I mean, at the moment I'd rather clean the brush when it's safe, because with my Alistar, I can just heal up again and so those traps won't be in the way if there is an emergency. But I just want to know if this is really the right way to go, or if I should instead leave them there?
I usually consider the following:
That is to say, it impedes your placement near your tower or prevents the carry from having a good spot to farm. If YES, remove it ASAP.
Usually bushes are a frequently used place for traps. In there, you need to consider having vision on it. In fact, even with a ward up, you're more likely to get caught inadvertently. It can be a good thing to remove those traps, but only if it is safe and you can afford loss of mana/health do to so.
If YES, that could mean the area is not warded. If you are sure of this, it could be useful NOT to remove the trap. If the jungler is aware of its position (verbally or visually with a ward) it could provide a better surprise effect for ganks.
Caitlyn can set up a maximum of three traps. Sometimes it's better to see the three traps rather to risk being caught in hidden ones. Example, if three traps are in the two botlane right bushes (or on the field), you can safely go in the river bush to put some ward.
In summary, if the trap is a real threat to your carry: remove it. Everything else is trivial and depends on your play-style. If you have to make extensive use of trapped area, you should consider cleaning so as to acquire full efficiency.
If its safe and you are not worried about loosing a small amount of health take it out. Just remember that they might use it as an opportunity to launch an attack, if Cait is nearby she will probably Q you, if is Taric or anyone with a stun you could get stunned for long enough to take some serious damage.
I would say in general if you have them pushed to take it out, as you said ali can just heal the damage tone trap will do, just watch out for anything else that being seen might cause.