This phrase raises similar issues to those in your earlier thread Huge car theft. In English we don't naturally form constructions like this for ad hoc descriptions, by which I mean descriptions of something particular, unique or transient, rather than general. A twenty minute late bus is not a kind of bus, it's the description of a bus in a certain situation. For this we would use a relative phrase or similar, such as sound shift has given. I have to say though, that I would like to see your phrase in a full sentence to decide how the situation would best be described.
Copyright gives a good example of the type of description where we do put this kind of descriptive phrase before the noun; e.g. ages, heights, etc. I guess there are other constructions which may be natural, for example, "an out of work man". All these phrases describe a permanent or lasting condition, or innate quality, rather than a very transient one (as in your bus), which may also be that factor that makes them acceptable. Another example is "an over the shoulder hairstyle": this is a type of hairstyle and "over the shoulder" describes an innate quality that makes it what it is.