I had to deal with this in a previous position with a very elderly volunteer who had trouble making it to the bathroom and had a few accidents. (She preferred to pretend nothing had happened so would decline when we offered her a change of pants, etc). It was not an easy subject, but as we were in a health care facility, were able to couch the conversation primarily as a policy one - our vulnerable patients need to be kept safe in a clean environment, can't do anything to compromise their health, etc. I was volunteer coordinator, but asked the colleague who worked more closely with her (and who the volunteer knew was aware of the accidents) to initiate this conversation, to not embarrass her further by bringing in a group to talk about it. Our troubleshooting was just to offer to keep a change of clothes there for her, just in case, and to make it clear that without changing, she wouldn't be able to stay to finish her shift if it happened again.
I have no idea your exact situation, but I imagine it differs! Perhaps the useful takeaways are, 1.) try to find a way to tie the conversation to policy, mission, whatever, in some way so that you have language to fall back on; and 2.) if at all possible, have someone already close to the volunteer have the conversation, if the alternative is going to make it clear that this has been a conversation around a meeting table and make it even more embarrassing.