"bidjar" bidya = "a state of repose" sleep:  Grey 1840 [:13:35] [NYUNGAR]
"beedjar" bidya = "sleep" sleep:  Lyon 1833 [:381:25] [NYUNGAR]
"bidjar" bidya = "sleep" sleep:  Brady 1845 [:381:48] [NYUNGAR]
"bid-jak" bidya[a]g = "stinking; offensive" stinking:  Grey 1840 [:394:50] [NYUNGAR]
"Bidjak" bidya[a]g = "Stinking" stinking: Moore 1842 [:161:14] [NYUNGAR]
The suffix '-ak' [-ag] is the possessive. Thus bidya-[a]g might be 'sleep-of'.
Perhaps the connection is:
—a dead animal might be viewed as 'sleeping';
—a dead animal is often associated with an offensive smell.
In the above records extracts, original entries are given in double quotes (for the Australian, and for the English translation). These are followed in each case by a modern respelling and a modern standarsided translation. Each extract ends with source and language information. The main source for this post is Bindon, Peter and Ross Chadwick. 1992. "A Nyoongar wordlist from the south west of Western Australia / compiled and edited by Peter Bindon & Ross Chadwick." Pp. xi, 454. Perth: Anthropology Dept., Western Australian Museum.