I suppose there is no special reason for these abbreviations. I think it's only used to shorten it, even if bias is a short word. Some people tend to use abbreviations for Regards (Rgds) or Thanks (Thx), although the abbreviations aren't shorter than the words in full.
Gender bias is a scientific term. (racial bias might be as well) If you need this term for scientific reports the word in full is preferable. Abbreviations should be avoided when there is an acceptable alternative.
As to the usage of periods after abbreviations this website might provide you with useful information. There are quite a lot of rules regarding abbreviations, British and American English follow different guidelines in some cases.
Hope this helps,