I am still not sure if we were in the right place.  I had an eBird map zoomed in as far as possible and I found this sign-posted entrance.

We drove down the track towards Bird Billabong but the road got too rough for a 2WD so we turned back.

OK obviously people are meant to find birds somewhere around here!  Or at least fish!

We tried another direction which ends up at this boat ramp.  Not knowing what to do, we had to turn back and give up.  At least there were a few birds in the surrounding trees. 

Ironically, when we got back to Mary River Wilderness Retreat, we spotted the guide from Experience the Wild (his 4×4 was marked as such).  They are the ones who wrote the guide to Bird Billabong!  If I had printed out this page, we probably would have found the right place.  Good lesson to double-check directions and locations.  Or maybe we would have been ok if we had a 4×4.  Guess we will have to come back someday!