In your question you asked (a) how to structure the study, and (b) what are the dimensions of GB. I assume that by "structure" you mean "design"?
The question implies a study that involves measuring [dimensions of] GB...which further suggests a study designed around statistical analysis of the problem. May I suggest that you take a case-study approach instead? However, if you are looking to investigate the relationship between GB (as an outcome variable) and some type(s) of IVs, then you might be looking at a correlational design (e.g. regression analysis).
Fundamentally Green Business revolves around three interdependent dimensions: environment, economy and society. Hence, Green Business expected to maximizing the environmental value created, through a socially
empowering project, and over a viable and effective business model (issues of sustainability at Work without affecting the future generation of ecosystem,
reducing energy, water and waste to increase profitability by reducing costs as well producing Eco-friendly production)
Using the LEED principles as a guideline might be helpful. ( LEED = Leadership in Energy and Environmental Design ). LEED is a reference for Green Building, and reletaed to the structure, but the reference to what the requirements are, are easily transposible to a business as a whole. I believe it is worth checking it out, as a reference to your studies! Hope this is helpful to you.