Yes mate, take your bike definitely.
I have ridden Pomingalarna (Pomi') a couple of times and it is a great cross country area with a lot of trails packed into a small space, there are some nice flowy sections especially the last 2ks or so. Pomi' is on the outer west limits of town, behind the golf course directly opposite the turn off to Albury, enter via McNickle Road.
A mate of mine also rode a track behind the Uni that had jumps and drops but I haven't, you would need to ask around about that one.
Cheers. Dale, Albury.