Career Advice needed

Hello All
I would be really obliged if anyone experienced could give an answer or advice.

I am an electrical engineer with 3 years of experience in telecom and automation. Also included have been a lot of project management. I just switched job and joined a technical proposals team at a prestigious firm.
I have always wanted to align my career in the field of business management and I also want to study further in this field.

First Am I going in the right direction in terms of career?
How should I proceed with my education and do i need it e.g: MBA (because I really want to do this).
Should I go full time or part time and what other options are available except MBA

Thanks