I would suggest not lunging her all that much. it's hard on the joints, and she's an old girl. Take it easy on her. As for bonding...that comes with fair riding, feeding, cleaning, grooming, and daily handling. You can also lead her and hand graze. It makes you a herd of two. Maybe teach her some tricks.
Nice suggestions on bonding activities.
About lunging: That was my Arabian mare's mainstay physio when I was still riding her in her late 20s. I free lunged her on soft footing in a good-sized round yard, at least every second day, with work mostly at trot and canter, and some walk breaks, in 15-25min sessions, enough to dilate the blood vessels and raise a light
sweat. Lots of transitions and direction changes, which she liked. The key thing with any exercise is to do it consistently rather than sporadically, and to build up gradually when the horse has had a spell so you don't overtax. The lunging was super for my mare's back muscles (which need extra TLC in old age) and general conditioning, and helped her body deal with ridden work, kind of like my Pilates helped me.
And like tinyliny said, I had to make sure she didn't overdo it when riding. Noone had ever told her she was getting old... and she still wanted to gallop up every hill, but I no longer let her. She was allowed to trot all she liked and canter, but no flat tack or heavy sand work anymore, and no heavy sweating allowed.
My mare at 27:
Wonderful bonding and trick training on this site: Augustus the Mustang | Adventures of Augustus the Mustang
Really worth looking at. This HF member is training a mustang and the level of relationship and cooperation between her and her horse after only a couple of months is wonderful. She plays all sorts of games with him and he lies down on request and she can sit on top of him lying down etc. Videos of all that are on this site but you may have to dig into the archives to see all that cool stuff.