The other suggestions are not bad either but I would prefer this one:

"Dün gece kötü bir rüya gördüm."

Instead "dün gece" if you say "geçen gece" it will be the night before last night. Smillarly "geçen gün" is the day before yesterday.

Yes düş is more poetic. Also düş implies more like an imagination.

In English there is no difference between a dream while you sleep and a dream that you have while you are conscious.

When Martin Luther King said "I have a dream" he didn't mean a dream he had while sleeping. In Turkish we devide them.
'rüya' is strictly for a dream that you have while sleeping.
'düş' is mostly for an imagination when we don't sleep. It can be intuitonal or fictional but in any case we are conscious. The images are in front of our eyes. We have seen them in some ways. Maybe something has inspired us to see the image.

"Dün gece kötü bir düş gördüm." is more likely to be a dream/imagination that you have while not sleeping. If you had given me this sentence and would ask me whether or not the person is likely to sleep during this action I would say 80% not sleeping and 20% sleeping.

Hayal is different than both rüya and düş. Hayal strictly has nothing to do with sleeping. Hayal includes hope for something to become true. "Hayal etmek" and "hayal kurmak" are both common verbs. Also "hayal kırıklığı" means disapointment and "hayalperest" means "dreamer" (the kind of person who is in a dream world).
I would translate Martin Luther King's speech with hayal: "Bir hayalim var"

So I guess that you could translate "düş görüyor" with "she's daydreaming"?

Elisa,
This could be. Assuming someone's dog has died and the person starts to see an imaginative dog walking inside the house. She is talking to a dog that already died. In this case obviously we can't use rüya since this is not a dream in sleep and we shouldnt use hayal as hayal is something that you imagine and hope it will become reality.

In this example and in mental illnesses, in drug imaginations and in transendental imaginations I would use düş görmek. But of course düş is not limited with this. It is also used for creative imagination in arts and literature.

Said that I must add that the main translation for the verb "to imagine" would be "hayal etmek". Düş and any verbal forms of it are not so common.

Then how does the song of Sezen Aksu translate?

Yürüyorum düş bahçelerinde..

I am walking in your gardens of dreams?


So reading the comments before, this could mean she is saying it to a man that she loves/that loves her, and they are both dreaming poetically about eachother? Kind of?
(not mentioning the rest of the lyrics, just based on this one sentence).

Or what else could be meant? because it's also like hoping about something.

Rüya is also a girl's name, right?

yuruyorum ruya bahcelerinde..

i am walking in the gardens of dream

ruya bahceleri = gardens of dream called "tamlama" in turkish grammar so ruya bahceleri-nde ---> in the gardens of dream.

and yes Ruya is a girl name.. very nice name in deed