It’s possible that she was so unsteady they were leery of her tilting her head back to drink from the bottle and gave her a glass to sip from instead.
That's what I think. It was water. I don't think we should try to read too much into little details like drinking from a glass versus a bottle. Let's not give the other side the opportunity to ridicule us over something like that. Instead, the video of Hillary's coughing spell is damaging enough. The video speaks for itself.