Your exact requirements would be met by a 36V system using 3 18AH sealed lead acid batteries.
I know because the specs you listed were exactly what I had with my kit using said voltage and batteries.
If I were to do an electric bike again, I would just build it myself with a motor right behind the seat and a chain going down attaching to the left side of the rear sprocket.
I saw a really nice electric bike a few weeks ago.
PHOTO HERE
If you are really interested in how that one works, I could pester the builder with any questions for you.