I've found what I was looking for : instead of

Url = string.Format("https://developer.api.autodesk.com/oss/v2/buckets/{0}/objects/{1}", bucketKey, outputName)

I needed following syntax :

Url = $"urn:adsk.objects:os.object:{bucketKey}/{outputName}",

Now it uploads my resulting zip file to my specified bucket.

Hope this helps anyone else