In my current project I want to use Behavior Driven Development (BDD), on both levels of business requirements application level tasks.
Is it all right to wrap (group) my internal BDD specs into my high level specs so clients would see that business requirement is done (all internal specs in that requirement passed) but don't actually see my internal specs?
Do you mean "should I put a bunch of test case source code in my specification?" (BDD is essentially a reframing of TDD)
Then the answer is almost certainly NO. Your client probably cares about getting a system that does what she wants, and what she wants is almost certainly not what she asked for in the first place.
Just put the software in the hands of your client as soon as possible to get feedback. Agile software development practices are all about clients giving feedback early and iterating the requirements quickly.
A spec is only useful for two things: a support for discussing requirements (before it's done), and a tool for finger-pointing (when the client says the software does not do what she needs). The former is constructive, the second is not.