Hello,
As you don't know what was in the mind of the designer, I think trying to calculate a minimum clearance is virtually impossible. If you want to know the behavior close to other materials (both conducting and non-conducting), you should measure it (that means both VSWR/reflection coefficient and radiated power or gain). .
It can be done with relative primitive means, but if you are not into RF it will take significant time to acquire the knowledge, especially when you don't have somebody at hand who knows what to do. Having an antenna analyzer or (vector) network analyser and a signal source (your bluetooth module?) makes life easier, but still things can go wrong.
Just basic antenna knowledge isn't sufficient. You need to assess the influence of reflections and influence of the cable that feeds the antenna (if you use a VNA or (scalair) antenna analyser).
In my opinion, even if you follow application notes or datasheet guidelines, you should check your antenna.
If this is a once only problem, and you don't have lots of time, hiring an expert may commercially be attractive.