Regardless of whether she has the capability to build a bio warfare program, I doubt that China has the will to do so. You can claim nuclear weapon as a strategic defensive weapon, but you can't use the same reasoning to justify developing biological weapons: you can't scare someone with a consealed weapon. PLA only wants to be seen as a regional defensive power.
Another reason that China is deterred from acquiring bio warfare capabilities is that China was a victim of the Japanese biological warfare during the sino-japan war. I vividly remember watching those horrifying pictures from the famous tv shows about the Unit 731 in my childhood. The biological weapon, IMO, is one of the most inhumane weapons that mankind has ever conceived.
Finally, aquiring such capabilities does not fit in China's strategic plan. China's military power has seen repid growth in the past 20 years, but the main objective of the military is not to eredicate an entire enemy race. China has always fought wars with exit strategies (unlike America), ones that you can slap your ememy without developing into a fist fight. In such warfare, biological weapons are of no use.