Closed loop system stability with Bode
You can easily find the phase margin by simply solving for the open loop gain from the closed loop gain.
If \$F(s)\$ is the closed loop transfer function, and \$G(s)\$ is the open loop, then:
$$ F(s)=\frac{G(s)}{1+G(s)}$$
so
$$ G(s)=\frac{F(s)}{1-F(s)}$$
You can work out the closed loop gain that corresponds to the open loop unity gain with a particular phase margin.

and just look at the closed loop gain bode plot to see where your loop is.  The one you posted seems to have a phase margin of about 70 degrees.
The bode plot is not the easiest way to do this, if you plotted the closed loop gain on a polar plot, then the table above would be a curve and you could just find the point of intersection.