GC-MS is not a viable technique for polymeric material. If you want to analyze the beta-hydroxybutyrate itself then GC-MS will work fine, but not for polymeric mixtures.
what do you want to learn about your samples? As already noted, polymers do not volatilize well, but if there is something in the polymer that you seek, a bit more detail in your inquiry would help.
Brandl, H., R. A. Gross, et al. (1988). Pseudomonas oleovorans as a source of poly (β-hydroxyalkanoates) for potential applications as biodegradable polyesters. Applied and Environmental Microbiology 54(8): 1977-1982.
Wu, G. F., Q. Y. Wu, et al. (2001). Accumulation of poly-β-hydroxybutyrate in cyanobacterium Synechocystis sp. PCC6803. Bioresource Technology 76(2): 85-90.
1. Weigh 4 mg of sample into a 10 mL Teflon tube or glass reacti-vial (check seal) .
2. Add 1 ml of chloroform, 0.85 ml of methanol, and 0.15 ml of sulphuric acid.
3. Heat at 100oC for 140 min.
4. Allow to cool then add water (1mL), shake and separate phases (centrifuge).
5. Remove organic layer into fresh 10 x 1.2 cm test tube.
6. Wash with water allow phase separation.
7. Remove organic layer into fresh 10 x 1.2 cm test tube.
8. Dry extract with small spatula full of sodium sulphate and decant into fresh 10 x 1.2 cm test tube.
9. Transfer 400 µl to auto-sampler vials for GC/MS analysis.