I think that "career in synthetic biology" and "involved in planning" both express very vague ideas. There are significant differences in what you will be able to do with a Bachelor's, Master's or PhD, depending on what exactly you end up doing.
I entered a PhD program in biology for no better reason than that I felt awed and fascinated with science and had done really well in science subjects as an undergrad. Grad school seemed like a natural extension of that effort.
In retrospect, my motivations for pursuing a PhD were horribly naïve and easily the greatest challenge that I faced as a grad student was that of defining why I was there and where I wanted to go with my degree. So, to address the issue of vagueness in your question, my first piece of advice is to have a firmer idea of what you want to do. Plans will change, but simply having a plan (a real plan) might provide an anchor when you need one.
As to what you can do with the various degrees, I can't precisely answer your question, the way you've phrased it, but I can give you a general idea.
A bachelor's degree in biology will not get you far in a lab setting. Among the lab techs I've worked with, even most of them have master's degrees. From what I've seen, this holds just as true for academia as for industry.
It's a little unclear what you mean by "planning", but most of the admin that I work with, who are involved in planning our various projects also hold advanced degrees, typically in science, business or public health. I see a strong representation among the management at my institution (Columbia University) of PhD scientists, who left the bench for something less life-consuming, while still wanting to have a hand in research. These people are frequently grants managers or program directors.
As I mentioned earlier, the lab techs around me generally hold master's degrees. When I was considering quitting my PhD program after the master's component, a friend in industry advised me against it, if I ever thought that I might seek work in industry. The picture that he painted was that in industry, a master's degree makes you overqualified for many of the tasks that you can expect to be hired for, but underqualified for significant future career advancement.
Obviously, you shouldn't feel limited to academic vs industrial research tracks. There are plenty of other options out there. Maybe look up people's blogs that involve synthetic biology or whatever other topics of interest you might have to get a wider view of what people who have expertise in the subject are doing.