Can you suppress a bad memory or traumatic event to the point that you don't remember it?

Memory: Well, not intentionally. However if you involved in a significant trauma especially loss of consciousness you may forget the event. It is called amnesia.

Yes - sort of: If the traumatic event is stored in memory it can/will likely be recollected at a future time. It is possible to actually not be able to recall a memory that is there, but actively suppressing one is not a good strategy for coping. It is better to deal with trauma by talking and processing it out in a supportive environment than to try to suppress it.

Memories: Traumatic memories can be repressed, but more likely they cause more conscious suffering. When trauma occurs and one sees it, the neurotransmitter acetylcholine "stamps" these memories in making them even more difficult to suppress or repress. Better is to deal with the trauma memory in psychotherapy with a licensed mental health practitioner.

Memory: Old psychoanalytic model talked about the mind as having 3 levels; conscious, subconscious & unconscious. The first is where events are kept in our awareness, the second is where memories or events are suppressed & they can be recalled down the road, and the third is where they are repressed & can be kept there indefinitely or can emerge later on, depending on the event currently at hand.