When you run the model with Bode Plot block, with "save data to workspace" enabled, you get a variable sys, or whatever name you specified for it. sys is a structure, like you said. It contain frequency response information in the form of state-spaces matrices A,B,C,D as well as block name and snapshot time when linearization was computed.
To access state space matrices type
sys.values
To get magnitude, phase and frequency data from the bode plot:
[mag,phase,w]=bode(sys.values);
Recreate Bode plot:
semilogx(squeeze(w),20*log10(squeeze(mag)))
subplot(211)
semilogx(squeeze(w),20*log10(squeeze(mag)))
subplot(212)
semilogx(squeeze(w),squeeze(phase))
