I just got an old mare that is sway back.
I was wondering is there's anything that can do to improve it.
And if light occasional riding would hurt her.
Also what could I do to keep the saddle from bridging?
We have a 35 year old mare with slight sway-back and she is ridden once a week, just used for the occasional lead rein. The lesson is only 20 minutes, mostly walk and some trot.
Doing belly lifts with her (running your thumb firmly down her mid-line under her belly until she flexes her stomach and lifts her back) can help to strengthen her stomach muscles which can help to prevent further swaying (and maybe even correct it to some degree, depending on why it's swayed). A swayback pad that is properly shimmed can stop the saddle from bridging, but like others said, the severity of it will dictate whether riding is wise or not.
Without knowing the severity of the sway (ie pictures) it's really impossible to say what may or may not help and how much it may/may not hurt her to be used.